Eight citizens and several council members spoke against renaming the bridge, which is unofficially named after pioneer Alexander Young.
KXRO reports the vote against the Cobain rename drew applause from the audience at Wednesday's council meeting. Some people were concerned about memorializing the grunge rock musician because of his drug use, suicide and negative comments about his hometown.
The council did vote to name a small body of land on the Wishkah River the Cobain Landing.
One of Cobain's biggest hits with Nirvana was a song called "Something in the Way" which recounted a time the musician was homeless and living underneath a bridge.