As your altitude increases, your fpm should decrease, as there's a less of a "bite" to the air..  Say in the 737, you takeoff initially at 3500fpm.  On the climb you go back down to 3000fpm.  At around 12000, you bring it down to something lower, like 2500fpm.  You keep doing this at certain increments, or as checklists provide, until you hit your cruising altitude.

The reason why your angle of attack increases is because the autopilot is trying to keep the fpm you set in the vertical speed set.  The air density up there is lower than it is down here, so as stated, there's less of a "bite".  You need to compensate this by decreasing your fpm during your climb.

Hope this helps..