What time is 0337 in military time?

0337 (or 03:37) is 3:37 AM.

The other way round: 3:37 AM in military time is 0337, said “zero three thirty-seven hours.”

Military time	0337 hours
24-hour clock	03:37
12-hour clock	3:37 AM
Said out loud	“zero three thirty-seven hours”
Minutes after midnight	217
Share of the day gone	15.1%

How to convert 0337

The hour is 03, which is before 12, so it's a morning time: drop the leading zero, keep the minutes (37) and add AM. That gives 3:37 AM.