As was already said, trainers are designed to fly that way. When I was under instruction, with my instructor on a buddy box (if you are not using a buddy box with an instructor, you are losing a valuable tool.)

An instructor should figure what is going on and why. In this case, once airborne, cutting the throttle to about half, then adjusting the trim for a straight and level flight should do it for you. The first thing you should do after take off is to trim at desired flight speed. Any changes in the throttle after that (any changes.. decresase and it will lose altitude. Add throttle and it will gain altitude) will result in a required re-trim for straight and level flight.

Simple as that.

CGr.