Two people conducted a citizen's arrest on a man in his 60s after he allegedly tried to rob a bank in Perth's CBD on Friday.

The 63-year-old allegedly entered a Bankwest on Murray Street around 11am and demanded money from a teller while suggesting he had a weapon.

A police spokeswoman said when the teller refused, the man pushed them and grabbed a sum of cash.

"The man ran from the store and was stopped by two members of the public who held him until officers from the Perth Bike Team arrived," he said.