There was no immediate claim of responsibility for the bombs, which went off within about an hour and included one planted under a seat at a bus stop outside a shopping mall which wounded 15 people, two seriously, they said.
''There was a big bang and people started screaming and running.
I saw people with blood all over their legs and faces,'' said Chalermsak Sanbee, 17, who was standing near the bus stop.
Another went off near a police booth, wounding two people, and a third was placed in a trash can at a market in the port district and wounded five, including a 10-year-old child, police said.
The bomb outside the shopping mall near the Victory Monument in the centre of the Thai capital appeared to have caused the largest number of injuries, they said.
Another went off in the parking lot of a shopping mall on the road to Bangkok's new airport and police closed the centre down, but plans for the New Year countdown in the city's main shopping district were going ahead with increased security.
Militants in the Muslim-majority three southern provinces of Thailand near the Malaysian border have used the tactic of setting of a series of bombs over a short space of time in towns in the region.
They are not known to have launched attacks outside the region so far despite constant fears they would.
More than 1,800 people have been killed in the latest separatist insurgency in the far south, where most people speak a Malay dialect, since it erupted on January 4 2004.
Reuters SSC DB1843