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-βM)×[(u0+αHu0×M)·]M, where u0 is the direction of the injected current, αH is the Hall angle and β is the non-adiabaticity parameter due to spin relaxation. Since αH and β 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.

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