This sort of thing happens with something called the dawn phenomenon. Its where your body dumps some sugar to get you ready for the day. I don't seem to suffer from it at the moment but I am sure someone who does will be along soon. Have a quick Google search.
Edit: Also as you are new, dawn phenomenon may not be the issue, it could be your basal dose. Your basal dose may need tweaking. I took a while to get my basal correct.
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