Singular problem and adjustment time problem of traditional Terminal sliding mode control are considered for second order nonlinear system with uncertainty. The reaching law is used to improve the convergence rate of reaching the sliding surface. Non-singular Terminal sliding mode control method based on exponential reaching law and two controllers are proposed in this paper. The singular problem is avoided and the convergence rate is improved. Simulation results show that the system converges to the equilibrium in a short time by the designed controller, and also show the effective of the proposed method.