Abstract: By using the method of geometric analysis and some important inequalities,  we studied the local characterization of four-dimensional complete gradient almost Ricci solitons satisfying certain conditions involving either the anti-self-dual or self-dual part of the Weyl tensor, and proved that such solitons were locally warped product structure with three-dimensional  constant sectional curvature fibers or three-dimensional Einstein fibers.

Key words: gradient almost Ricci soliton, Weyl tensor, warped product