This paper addresses two composite learning controller designs of quadrotor dynamics with unknown dynamics and time-varying disturbances using the terminal sliding mode. For unknown system dynamics, the single-hidden-layer feedforward network is employed for approximation which provides the information for the disturbance observer. Based on composite learning using neural approximation and disturbance estimation, the terminal sliding mode control (TSMC) is synthesized to obtain the finite-time convergence performance. To overcome the singularity problem, nonsingular TSMC is proposed. The closed-loop system stability under the two proposed controllers is presented via Lyapunov approach and the systemtrajectory will converge to the region caused by approximation error and disturbance estimation error. Simulation results demonstrate that the composite learning can efficiently estimate the system uncertainty and the tracking performance under the proposed controllers can be enhanced.