All applicants must take a civil service exam on Saturday.
Police Chief Charles Wiley says 739 people met last Thursday's deadline to apply, but it is unknown whether Galveston, slammed by Ike in September 2008, will fill the 15 jobs.
City leaders are trying to determine whether the island's improving finances can mean an end to a hiring freeze since Ike damage sent property values plummeting.
Wiley says the police department has 170 officers when fully staffed.
The Galveston County Daily News reported Monday that starting annual pay for a police cadet with no experience is $30,000.