A construction company has taken a Brunswick man dubbed 'Australia's Spiderman' to the Supreme Court to stop him climbing cranes on their building sites.

Probuild Construction (Aust) Pty Ltd sought an injunction on Thursday, restraining Bryce Wilson, 23, from entering any of their construction sites in Melbourne.

In their statement of claim, the company said that on June 22 Mr Wilson illegally entered the Abode construction site in Russell Street where a 34-storey apartment block was being built. The statement said Mr Wilson climbed on to the site's equipment, including a tower crane, damaging it.

"The defendant (Mr Wilson) took numerous photos whilst on the plaintiff’s (Probuild’s) crane on the site and uploaded those photos to his Instagram profile under the user name ‘drjft’, a social media photo sharing platform ...,’’ the company said.

Probuild said a story featuring Mr Wilson appeared on a television station’s website the next night titled ‘Melbourne’s Spiderman strikes again’.