Autonomous navigation of quadrotor is required by many application scenarios, such as exploration, search, and rescue. The trajectory planning algorithm is the core of autonomous navigation, which can undoubtedly greatly enhance the safety of flight.In this paper, a trajectory planning framework based on B-spline and kinodynamic search is proposed. This framework can be used for a limited-sensing quadrotor to plan safe and dynamically feasible trajectories in unknown environments, and the flight is safe and effective along with these trajectories. First, a B-spline based nonuniform kinodynamic (BNUK) search algorithm is proposed to generate dynamically feasible trajectories efficiently. The characteristics of nonuniform search make the generated trajectories safe and reasonable time-allocation. Then, a trajectory optimization method based on control point optimization is proposed. The trajectory generated by BNUK is further optimized by solving a quadratically constrained quadratic programming problem. The smoothness of the trajectory is improved, and the control cost is reduced. Extensive analysis and comparative