Authorities say that lights needed at night are not working on about half of the two-mile span.
City officials are considering how to proceed.
City spokeswoman Alicia Cahill said Monday that officials believe the 40 or so affected lights just need to have the 450-watt bulbs replaced.
The Galveston County Daily News reported Tuesday that the cost is about $450 apiece. The city also must rent specific equipment to reach the bulbs.
Cahill says the city council would need to approve the replacement project if the cost tops $15,000. She says another issue is that city workers suspect electrical components more complicated than bulbs have failed.
The causeway, about 45 miles southeast of Houston, opened nearly three years ago.