There was a brief civil war or at least a strong political split between him and Tibni, where there was some struggle as to who would become king. (1 Kings 16:21-22). Tibni died, somehow, and Omri became king.
Omri was a wicked king as well, following in his father's footsteps, and was comparatively more evil (1 Kings 16:25-26).
The entire story of Omri is in 1 Kings 16:15-28.