For the class of uncertain nonlinear systems with external disturbance in the big initial state, a nonlinear term with adjustable index is added into the traditional terminal sliding mode control, and a new fixed-time nonsingular terminal sliding mode control method is proposed.The traditional linear sliding mode, Terminal Sliding Mode (TSM) and Fast Terminal Sliding Mode (FTSM) are all special cases of the new sliding mode;and it is proved that the new sliding mode converges in fixed time when N>1.An analytic expression of the upper bound of the convergent time is obtained, which is independent of the initial state.It is proved that the scheme is superior to FTSM, and the influence of parameter selection on convergence speed and convergence time is further analyzed and the rule is summarized.Based on Lyapunov stability theory, a nonsingular fixed-time sliding mode controller is constructed for second-order nonlinear system, and it is proved that the control error can converge to any small closed ball at fixed time.Simulation results of quad-rotor aircraft attitude control have demonstrated the superiorities, such as faster convergent speed, stronger robustness and smaller steady error.