A magnetostrictive torque sensor includes first and second magnetostrictive films which are provided at a shaft and have different magnetic anisotropies; a first measurement coil and a second measurement coil which face the first magnetostrictive film; and a third measurement coil and a fourth measurement coil which face the second magnetostrictive film. A torque applied to the shaft is measured based on a variation in magnetic characteristics of the first and the second magnetostrictive films; and a failure of the magnetostrictive torque sensor is detected based on a first difference between output values from the first and the second measurement coils and a second difference between output values from the third and the fourth measurement coils. An electric steering system includes the magnetostrictive torque sensor for measuring a steering torque of the system; and an electric motor driven based on the measured magnetostrictive torque for steering the vehicle.