UN ambassador Nikki Haley said it was "hard to accept" that resolutions had been passed against Israel, a US ally, but none were considered on Venezuela.
She also said not enough had been done to criticise Iran, a "country with an abysmal human rights record".
Mrs Haley was making her first address to the council in Geneva.
"The United States is looking carefully at this council and our participation in it. We see some areas for significant strengthening," she said.
"Being a member of this council is a privilege and no country who is a human rights violator should be allowed a seat at the table.
"It's hard to accept that this council has never considered a resolution on Venezuela and yet it adopted five biased resolutions, in March, against a single country, Israel. It is essential that this council address its chronic anti-Israel bias if it is to have any credibility."
Venezuela has been in political turmoil for month and dozens of protesters have been killed.
Since its formation in 2006, the Human Rights Council has been a flawed body because its membership has included serial human rights violators such as China, Russia, Venezuela and Saudi Arabia.
That's been a bugbear of the US for years, and Nikki Haley said she would convene a side-meeting on Venezuela during her visit to Geneva to drive home the point.
But what seems to anger the Trump administration most about the 47-member body is what she described as its "chronic anti-Israel bias".
Writing in the Washington Post, she complained that the council had passed more than 70 resolutions against Israel but just seven against Iran. The Bush administration, believing the council would treat Israel unfairly, boycotted the body, a decision reversed by Barack Obama.
The message from the Trump administration is reform or we're leaving. Nikki Haley wants more competitive elections to the body rather than the regional blocs nominating candidates that are uncontested. It seems to have decided, for now, that it is better to have a seat at the table and to demand reform, rather than exit the council.
Criticism of the 47-member council was repeated on the Twitter feed of the US mission to the UN on Tuesday.
Speaking later at the Graduate Institute of Geneva, Mrs Haley said the US did not seek to leave the council but "we seek to re-establish the council's legitimacy".
The council is able only to order investigations and record criticism of countries it judges to have violated human rights, but it acts as a crucial diplomatic tool.
In recent months, it has issued resolutions on human rights in North Korea, Haiti and Myanmar, among other countries.
In March, the UK government accused the UNHRC of an "unacceptable pattern of bias" by singling Israel out as the only country subject to mandatory discussion at every session.
Israeli Prime Minister Benjamin Netanyahu has previously called the body "an anti-Israel circus which attacks the only democracy in the Middle East and ignores the blatant violations of Iran, Syria and North Korea".
And in 2013, Israel ended its working relationship with the group after it decided to investigate Jewish settlements in the West Bank.
Mrs Haley's comments came after an opening address in Geneva by UN human rights chief Zeid Ra'ad al-Hussein calling on Israel to withdraw from territories it captured in the 1967 war.
He condemned what he called "a half-century of deep suffering under an occupation imposed by military force".
Israel has occupied the West Bank, East Jerusalem and the Syrian Golan Heights since the war, 50 years ago this week. The UN also considers the Gaza Strip, which Israel pulled its troops and settlers out of in 2005, as part of occupied Palestinian territory.
Israel and the Palestinians blame each other for the failure to resolve the final status of the occupied territories after years of on-off peace talks.
Among the current members of the UNHRC is key US ally Saudi Arabia, which has been accused of rights violations, and whose accession to the group in 2013 was criticised.
The US says it is considering what part it will play on the UN's Human Rights Council, highlighting what it calls a "biased" stance on Israel.