A road surface friction coefficient estimating apparatus is provided for estimating a road surface friction coefficient of a vehicle that is traveling at a steady state. The road surface friction coefficient estimating apparatus basically has a driving/braking force controller, a driving force controller, a braking force controller (brake fluid pressure controller), a plurality of wheel velocity sensors, a wheel load sensor and a control unit. The driving/braking force controller sets a pre-selected force to be generated and calculates the road surface friction coefficient. The driving force controller generates a driving force in accordance with the pre-selected force. The braking force controller generates a braking force in accordance with the pre-selected force. The wheel velocity sensors produce a wheel velocity signal indicative of a wheel velocity. The wheel load detecting sensor produces a wheel load signal indicative of a wheel load. The control unit which is part of driving/braking force controller calculates a road surface friction coefficient based on the wheel load, the wheel velocity, and the braking and driving forces. The braking force is configured to cancel the driving force.