Surveillance video shows the suspect near the Korean Comfort Women Peace Monument on the Glendale Central Park grounds on Monday.
Police say the suspect wrote on the monument with a black marker, knocked over several potted plants surrounding it and then walked away.
The monument was installed in July 2013. It honors Korean woman who were forced into being sex slaves for the Japanese military during World War II.
The monument remains controversial because of the subject matter and there have been unsuccessful legal attempts to have it removed.
It was also vandalized in July.
At that time, an unknown substance was smeared on the statue and nearby flower pots were smashed.
If you have any information call Glendale police at (818)548-4911 or provide anonymous information to Crime Stoppers at (800)222-TIPS.