There is provided a steering assist device that allows a vehicle to avoid departing from a lane. A basic target current value setting unit sets a basic target current value on the basis of steering torque and a vehicle speed. A current compensation value computation unit computes a current compensation value for compensating the basic target current value on the basis of a lateral deviation and a lateral deviation variation rate such that the lateral deviation and the lateral deviation variation rate get close to zero. A target current value computation unit computes a target current value by subtracting the current compensation value computed by the current compensation value computation unit from the basic target current value set by the basic target current value setting unit.