Sounds like you have too much relief on the neck - it's bowing forward.
You need to tighten the truss rod, i.e. turn it clockwise (from the perspective of looking down at the top of the truss rod nut itself). Don't do more than a quarter turn :!: , then leave it for a few hours to settle before tightening again if necessary.
You'll probably find that once the neck is straight (or has just a little reflief) you'll need to raise the bridge slightly as the action will be too low at the upper frets. I'm assuming it has a Floyd/Edge trem, so you may need to slightly adjust the trem springs a bit too, to get the bridge how you want it. :)