A 32-year-old St Albans man has faced the Melbourne Magistrates Court charged with murder following the shooting death of a woman in Sunshine North last week.

It is alleged that the man shot his partner on Thursday night at the Sunshine North townhouse where they lived, before driving her to hospital where she died shortly after arrival.

The man was also charged with carjacking, attempted carjacking and firearms charges.

He was remanded to appear again on Thursday.