Detectives say 31-year-old Willian Andrade Jordan walked into the Bank of America on Grand Avenue in Baldwin around 1:15 p.m. Friday.
The man approached the teller and passed a note threatening her with a gun and a knife.
They say Andrade Jordan demanded $3,000, but the 29-year-old teller walked away from her station.
Officers say that's when the suspect ran off.
Detectives caught him on Long Beach Road in Freeport and arrested him a short time later.
Police say Andrade Jordan is responsible for several other robberies including banks in Rockville Centre, Garden City, and Westbury in early January.
William Andrade Jordan will be arraigned later this morning for multiple robbery charges.