There were 70 reports during the lambing season earlier this year compared with 45 over the same time last year.
Police Scotland said the crime, which involved dogs chasing farm animals, had previously been under-reported.
It said 60% of this year's incidents were detected and the dogs' owners reported to the procurator fiscal.
Most of the offences reported were in Aberdeenshire, Highlands and Islands and Lanarkshire.
Sheep were the most common animal affected. Other animals involved included horses and cattle.
In 79% of incidents, livestock were killed or injured, and on average this involved two or three sheep per incident.
Most incidents - 70% - involved only one dog and in 73% of cases the offending dog was local to that area, with more than half of all incidents involving a dog roaming free and where no owner was present.
Insp Jane Donaldson, Police Scotland's rural crime co-ordinator, said the rise in reports followed a campaign encouraging farmers and crofters to contact police about livestock worrying incidents.
She said: "Livestock worrying has previously been under-reported.
"Farmers were often reluctant to report incidents to police, particularly where there was a 'near miss' and no physical damage was done to their livestock.
"A significant part of the spring campaign was to get this message out to farmers and encourage them to report all incidents and I think that this is reflected in the increase in reported crimes.
"More accurate reporting has improved our understanding of the problem, increasing intelligence about the how, where and why these incidents are occurring."
Anne Gray, policy officer with Scottish Land and Estates, said: "We are very pleased with how successful this year's campaign has been and we will continue to support the initiative going forward.
"It is vital that livestock worrying incidents are reduced.
"No-one wants to see this type of completely unnecessary suffering and the higher the profile of these incidents the more, we hope, it will prompt the small minority of irresponsible dog owners to change their ways and ensure they know where their dog is at all times."
Reported incidents of livestock worrying have risen by 55%, according to police.