obuzimati

1. (of a feeling, thought) to overcome; to come over; to overwhelm
   Sve češće me obuzima tuga kad je gledam. — More and more often sadness comes over me when I look at her.
   Kad pomislim na ispit, obuzima me panika. — When I think about the exam, I'm overcome by panic.

The feeling or thought is the subject and the person is in the accusative: strah ga obuzima.