The nonlinear dynamics has posed a great challenge in the optimal control of quadcoptors. This paper applies data-driven methods to approximate the Koopman operator of the quadrotor attitude control system. The Koopman operator is a linear operator with infinite dimensions that can advance the nonlinear state dynamics linearly in a lifted space without compromising the operation range. The function basis and the propagation matrices to approximate the Koopman operator are learned interactively through Deep Neural Network (DNN). Simulations with the quadrotor attitude model in SO(3) are carried out to verify the model precision and the tracking performance using Linear Quadratic Regulator (LQR) with the lifted linear system. We compared the results with first-order approximation and Extended Dynamic Mode Decomposition (eDMD), which is another data-driven method that selects the function basis from a fixed library. Both data-driven approaches have notable advantages over the first-order approximation, while the system learned through the DNN has better precision and control performance than the eDMD.