The lines through Kapiti, Hutt Valley and Melling Line services have all been suspended, and are expected to stay suspended for several hours.
However, the Johnsonville line is still working.
A Transdev spokesperson said there was a power failure caused by a fault in the overhead lines, just outside the Wellington railway station.
"We're not sure on the cause. We'll have a full investigation on what's caused this.
"It looks like it's likely to affect services through peak this afternoon.
"We do recommend passengers look for alternative transport where possible."
The spokesperson said they were arranging buses to cover some services, but there weren't many available.
Southbound services on the Hutt Valley Line will be terminating at Petone while southbound services on the Kapiti Line will be terminating at Porirua.
Limited buses will be running between Wellington and Petone, and Wellington and Porirua.
Services on the Johnsonville Line and Wairarapa Line are currently unaffected, however there may be some delays.
