This paper proposes an estimation method of road-tire friction coefficient for the 4WID EV(4-wheel-independent-drive electric vehicle) in the pure longitudinal wheel slip, lateral sideslip and combined slip situations, which fuses both estimated longitudinal and lateral friction coefficients together, compared with existing methods based on a tire model in one single direction. Unscented Kalman filter (UKF) is introduced to estimate one-directional friction coefficient based on a modified Dugoff tire model. Considering the output results for each direction as a signal for the same target with different noise, MSE-weighted fusion method is proposed to fuse these two results together in order to reach a higher accuracy. The tire forces are estimated with the benefits of the 4WID EV that the driving torque and rolling speed of each wheel can be accurately known. The sideslip angles and slip ratios of each tire are calculated with a vehicle kinematic model. With the observed dynamic and kinematic states of vehicle and tire, the tire-road friction coefficients in different directions are estimated simultaneously based on the modified Dugoff tire model. Numerical results verify that the estimator designed is capable of estimating tire-road friction coefficient with reasonable accuracy, and the algorithm proposed in this work has good robustness and wide applicability under various maneuvers.