At 7th level, a Barbarian gains Feral Instinct:
... If you are surprised at the beginning of combat and aren't incapacitated, you can act normally on your first turn, but only if you enter your rage before doing anything else on that turn.
At first glance, it would seem that he cannot be surprised as long as he enters a rage but if you contrast this to the Alert Feat:
... You can't be surprised while you are conscious.
Feral Instincts merely says "you can act normally" and not that you can't be surprised as contrasted by the Alert feat.
If a creature with Surprise Attack (such as a Bugbear) hits an enraged surprised Barbarian, does it count as a Surprise Attack?