Cops were called to the A55 in north Wales after several reports of the canine sprinting through traffic travelling up to 70mph at 3am on Monday morning.
Officers claim they repeatedly tried to catch the dog but it slipped away every time.
Inspector Wareing said in a statement posted on North wales Police”s Facebook page: “The only safe option was to run the dog over at sufficient speed to ensure that it was destroyed and would not suffer.”
“At one point an officer tried to take hold of the dog but was then bitten.”
“The potential for a serious collision was present throughout, and in the circumstances there was no alternative way that officers could contain the dog and minimise risks to motorists.”
But their decision disgusted thousands who have taken to social media to accuse the force of animal cruelty.
Rohan Fox wrote on the force”s Facebook page: “Utterly disgusting. While I will happily support the police in many matters, you were wrong.
“To add at the end that this decision wasn”t taken lightly is revolting.
“As a force, you are a disgrace to condone this.”
Others said they would make a complaint to the Independent Police Complaints Commission.
However Emma Marie Haworth congratulated the police on the decision.
She wrote: “When the lives of multiple people are at risk compared to the life of the one dog it”s a responsible decision and wouldn”t have been easy for the officer who had to act upon it.”
The animal was running loose on the highway at varying locations between the Llanfairfechan roundabout and the Conwy tunnel.
The police have not confirmed whether the dog”s owners have been identified.