This paper presents a novel depth-based navigation system for quadrotors to enable autonomous flight in the GPS-denied environment. Our system leverages depth data transformed from the camera frame to the UAV’s local frame, and integrates this information with the onboard inertial measurements to counter drift of location signal. Using the radial basis function (RBF) filter, the system can efficiently identify passable area from the depth map, which are then used as inputs for a nonlinear model predictive control (MPC) framework. The integration of the perception and control components enables obstacle avoidance without requiring global positioning. Simulation tests demonstrate the effectiveness and robustness of this navigation system in maintaining safe, autonomous flight in unknown and GPS-denied environments. The actual experiment of traversing 100m long trees with an average speed of 5m/s also verifies the practicability of the proposed algorithm.