In a steering system 30, a transmission ratio R1 which is determined in dependence on the vehicle speed by reference to a transmission ratio decision map is multiplied with a first transmission ratio alteration gain g10 which is determined in dependence on the distribution of a traveling drive torque from an engine 11 to front wheels 14 and rear wheels 15, thereby to alter the ratio R1 of steering torque distribution from a steering handle 31 to the front wheels 14, whereby the variation of the steering feeling due to an increase or decrease in the distribution of the traveling drive torque to the front wheels 14 can be suppressed. Further, the transmission ratio R1 is multiplied with a second transmission ratio alteration gain g11 which is determined in dependence on the gradient of the road surface by reference to a second transmission ratio alteration map, thereby to alter the transmission ratio R1, whereby the variation of the steering feeling due to the variation of the gradient can also be suppressed.