This paper proposes a deep learning algorithm for solving the infinite-horizon optimal feedback control problem of a quadrotor unmanned aerial vehicle (UAV). The optimal control is represented by the stable manifold of the Hamilton–Jacobi–Bellman (HJB) equation in a 12-dimensional state space. Moreover, a deep learning algorithm is proposed to compute approximations of semiglobal stable manifold. The method is built on the geometric feature of the problem. The algorithm generates random data by solving the two-point boundary value problem of the characteristic Hamiltonian system of the HJB equation without discretizing the state space. The resulting data set lies on the stable manifold, and a deep neural network (NN) is trained to fit the data. The training process is conducted offline on a standard laptop without the use of a GPU. Generating feedback control for the quadrotor from the trained NN takes less than one millisecond, compared to several milliseconds required by existing methods for the same operation. The effectiveness of this approach is demonstrated by Monte Carlo tests and simulations in various scenarios.