They say the 72-year-old woman and 21-year-old man were pistol-whipped and robbed by the suspects around 9:45 p.m.
It happened at the Kroger at 5730 Seawall Blvd.
The victims told officers both suspects were Black males with facial tattoos. One was wearing all black and the other wore a red hoodie. They got away in a white sedan -- possibly a Honda -- and headed north on 57th Street.
The victims were treated for head and facial injuries at UTMB Health.
If you have any information about this case, please contact the Galveston Police Department’s Investigative Services Bureau at (409) 765-3770 or Galveston County Crime Stoppers at (409) 763-8477.