The fire broke out at Crawley Hospital in West Green Drive, Crawley at 13.36 pm.
It's believed to be in a sixth floor store room. There are no reports of casualities.
50 firefighters are involved with tackling the blaze.
More top news
Robert Weighton and Alfred Smith only became pen pals two years ago - and today Britain's oldest men both celebrated their 109th birthdays.
Simon's Blog - First Thing In The Morning....
Wednesday night's weather for the west of the region