A useful answer will depend on the context in which you want to use it, how technically precise it should be, etc.

One possibility is to use the term top of a/the hour:

From the top of the hour prior to the current hour to the top of the current hour.

Idiom definition:

at the top of the hour
Fig. at the exact beginning of an hour. (Alludes to the big hand on a clock pointing to the 12. Often heard on television or the radio. See also at the bottom of the hour.)
Every class in my school starts at the top of the hour. Our next newscast will be at the top of the hour.

McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. S.v. "at the top of the hour." Retrieved April 20 2015 from http://idioms.thefreedictionary.com/at+the+top+of+the+hour

A useful answer will depend on the context in which you want to use it, how technically precise it should be (need you worry whether now might be considered exactly x:00), etc.

Quite informally but plainly, you might use

The hour that began 60 minutes before the beginning of the current hour.

You might also use the term top of a/the hour:

From the top of the hour prior to the current hour to the top of the current hour.

Idiom definition:

at the top of the hour
Fig. at the exact beginning of an hour. (Alludes to the big hand on a clock pointing to the 12. Often heard on television or the radio. See also at the bottom of the hour.)
Every class in my school starts at the top of the hour. Our next newscast will be at the top of the hour.

McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. S.v. "at the top of the hour." Retrieved April 20 2015 from http://idioms.thefreedictionary.com/at+the+top+of+the+hour