The success of the two-mass system control problem heavily depends on the accuracy information of the load torque. In the paper, a radial basis function neural network structure is proposed to deal with load torque estimation. The estimated value is integrated with backstepping- sliding mode control to guarantee speed tracking performance in the presence of a non-rigid driving shaft. The stability of the closed-loop is proven analytically and illustrated numerically. In addition, the effectiveness of the proposed control is compared with a high gain observer-based structure.