A correlation coefficient computing unit receives front-left and front-right wheel-accelerations from high-pass filters, each having a driver-operating component removed therefrom, and computes a correlation coefficient therebetween. A computing-unit of upper and lower limits of a correlation coefficient of a population sets upper and lower limits of a correlation coefficient of a population. First and second correction-gain setting units set first and second correction-gains varying in accordance with running and driving states, respectively. A correlation coefficient computing unit of a population computes a correlation coefficient of a population of this time based on the correlation coefficients computed as above, a correlation coefficient of a population of the previous time, the upper and lower limits, and the first and second correction-gains. A coefficient of friction on road surface estimating unit estimates a coefficient of friction on road surface by comparing the correlation coefficient of the population of this time with a determining threshold value previously set according to the running state.