The trio were carrying knives when they targeted the Vesper Gate on Abbey Road at 11.15pm on Sunday night.
They were wearing balaclavas and threatened staff before taking cash from the safe.
They fled along Abbey Road in the direction of Abbey Walk.
Detective Inspector Richard Holmes, of Leeds District CID, said:
“This was a frightening experience for the members of staff to be confronted by these men. Thankfully they were not physically injured.
“We are carrying out extensive enquiries into the incident and would like to hear from anyone who witnessed anything suspicious in the area of the pub prior to the robbery, or who saw these men running off from the scene.”
Anyone with information is asked to contact Leeds District CID via 101 quoting crime number 13170541942 or call the independent charity Crimestoppers anonymously on 0800 555 111.