The Grammy award-winning artist said in a statement that he was choosing to "make a political stand".
He said reports of summary executions in the Philippines were "unacceptable to anyone who loves the rule of law".
President Rodrigo Duterte has vowed to eradicate drugs and urged citizens to kill dealers who resist arrest.
He was elected in May. In his previous role as mayor of Davao city, Mr Duterte built a reputation for blunt speaking and supporting the extrajudicial killings of suspected criminals.
James Taylor, 68, was scheduled to have played in the capital Manila next February.
"I don't think of my music as being particularly political but sometimes one is called upon to make a political stand," he said in a Facebook post.
"For a sovereign nation to prosecute and punish, under the law, those responsible for the illegal trade in drugs is, of course, understandable, even commendable; but recent reports from the Philippines... are deeply concerning and unacceptable to anyone who loves the rule of law."
Fans reacted with disappointment, but many praised the singer for his "integrity in adopting a principled stand".
"Thank you for your stand. I will miss seeing you perform but it's a small price to pay for standing up for one's principles," said Allan Victorino.
Another Facebook user Patricia Lyons, said: "We all need to take a stand, speak out and act on our truth."
But supporters of President Duterte criticised Taylor's "boycott" of their country.
"It's not our loss if he decided to cancel the Manila leg of his tour, it's his. James Taylor has missed the opportunity to perform before thousands of Filipinos, given the fact that he's now in the twilight of his career," said Wendell Sotto.
"Only fans will benefit from James Taylor's concert but good governance will benefit our entire nation," said Rendell Bata.
US singer James Taylor has cancelled an upcoming concert in the Philippines over reports of extrajudicial killings in the country's war on drugs.