Is there a new game plus for Mass Effect 3?

Yes.

After completing Mass Effect 3 you can re-import your Shepard after having completed the game. You'll retain your level, powers, and bonus powers, your credits, your Reputation/Renegade/Paragon scores, and all weapons, mods and armor.

Additionally, on repeat playthroughs higher levels of weapon mods are unlocked that are not available on your first attempt to save the galaxy, which is presumably quite helpful for inevitable insanity runs.

I believe that it will use the same format as the previous two titles. You will be able to begin the game again with all of your XP, skills and gear, but you will have to find fresh allies.

The annoying part of this -if I remember correctly- is that you can change your difficulty, but you cannot change your class or sex. So if you want to play a different class or swap between male/femshep you'll have to start all over again.