One theft occurred in the 1800 block of North Maple Street in Burbank at about 3:30 p.m. on Dec. 7.
The package had just been delivered to the home, leading investigators to believe the man may have been following the mail carrier.
In the video, the mail truck is seen parked in front of the home, but the carrier is out on foot making other deliveries at the time, police said.
The department on Friday tweeted another incident that involved the same suspect in the same area on the same day.
Burbank police said they encourage both residents and mail carriers to be vigilant of suspicious activity during the holiday season, when porch pirates are more common.
Anyone with information on the suspect is urged to call 818-238-3210.