Porirua City Council website has been under attack since the weekend.
The website has been shutting down automatically for about 20 minutes to stop the suspected Denial of Service attack from damaging its system.
The council's corporate services manager Roy Baker said each time the computer-generated IP address of the attacker is blocked, it changes to a new address.
It seemed the attacker wants to put malicious codes into the council's databases.
Attacks like these are not uncommon, Mr Baker said.