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The permanent magnet synchronous motor (PMSM) control is demanding task because, which is a nonlinear multivariable coupling system. The vector control has been widely used in the control of PMSM system, where the rotor position information is needed for close loop control system. The mechanical sensors are used for rotor position, which increased the cost of the system. These sensors can be eliminated by adopting the sensorless control methods. In this paper a new continuous terminal sliding mode observer (CTSMO) based speed sensorless control method is proposed, which is substitute of the conventional SMO (CSMO). The suggested the CTSMO is robust against parametric change and load disturbances, which is used to estimate the speed and rotor position from the back EMF (BEMF) of the PMSM system. The conventional SMO needs the low pass filter (LPF), position compensation techniques and sigmoid function instead of sign function to decrease the chattering phenomena. To eliminate the chattering phenomena effectively the new CTSMO based speed sensorless method is designed in this paper, which has also ability of minimization of the speed and rotor position error. The stability of the proposed technique is analyzed by Lyapunov function, the simulation have been carried out for the validation of the suggested technique.