Current-induced spin torque and magnetization dynamics in the presence of spin Hall effect in magnetic textures is studied theoretically. The local deviation of the charge current gives rise to a current-induced spin torque of the form (1 - beta M) x [(u(0) + alpha(H)u(0) x M) .V]M, where u(0) is the direction of the injected current, alpha(H) is the Hall angle and beta is the non-adiabaticity parameter due to spin relaxation. Since alpha(H) and beta can have a comparable order of magnitude, we show that this torque can significantly modify the current-induced dynamics of both transverse and vortex walls.