Matthew Hardy, 23, of the 3700 block of Richmond Avenue, is charged with three counts of purse snatching, as well as a burglary in the past month in the 3700 block of Parkway.
Hardy is known to frequent the Highland and Broadmoor areas of the city, police said.
Hardy failed to appear in Caddo District Court on Tuesday to face two felony theft charges in connection with the theft of videos and games from Blockbuster video, and for stealing checks from his father and trying to cash them.
Police have already arrested one man in the case.
Jerry Wayne Peters, 21, of Shreveport surrendered to police and was booked in connection with a May 1 purse snatching outside Belk's Department store on East 70th Street and with purse snatchings on April 21 and April 29 at the Walgreen's on Southfield Road.
Police believe a third man is also involved in the crimes. His name has not been released.