A man has been charged with murder following the fatal shooting of young Yarraville couple Veton and Lindita Musai on New Year's Eve.

Osman Shaptafaj, 55, was on Thursday charged with two counts of murder. He remains under police guard in hospital with gunshot wounds.

Lindita and Veton Musai. Credit:Facebook

Mr Shaptafaj, from Altona North, is Ms Musai's estranged father.

He did not appear in court on Thursday and his case will return to court on May 14 for a committal mention.