This paper proposes a sensorless speed control approach of induction motor applying full-order terminal sliding-mode control theory. The speed control system consists of three feedback control loops, i.e., the speed-, flux-and current-loops. The related controllers in these three feedback loops are designed using full-order terminal sliding-mode to enhance the robustness and dynamic performance, eliminate the singularity, and attenuate the chattering. The virtual control technique is utilized in the outer-loop speed controller to compensate unmatched uncertainties in the system, such as load disturbance and some parameter variations. The integral-type continuous control law with gain adaptation algorithm guarantees that the current references are smooth. In the inner-loop controllers, the actual voltage control signals can force the tracking errors of the currents to converge to its equilibrium point within finite time. Meanwhile, the full-order terminal sliding-mode observer is designed for estimating the flux and speed of the motor simultaneously. Finally, the experiment results have demonstrated the effectiveness and feasibility of the proposed sliding-mode controllers and observers for the sensorless speed control of induction motor.