Mine can do this too- I use an insulin pump, and my highest basal rate is actually the middle of the night/early hours of the morning.
It may be linked to what you have eaten: a large meal, or one that has more fat in it e.g. takeaway will take a lot longer to digest. If you give insulin to cover the meal, this will cover for say 2 hours whereas the meal might take 4 hours to digest, in which case you BG will increase, sometimes dramatically. With the pump I simply set a long dual wave, so the insulin goes in over a longer period of time. With injections, it might be worth splitting it eg giving some of your insulin initially to cover the meal and then some a little later.
Your DSN will be able to advise you on this