Recently, the robotics community introduced a novel quadrotor design equipped with a pogo stick mechanism. This robot can establish rapid ground contact and save thrust by bouncing, which can improve endurance for near-ground tasks and enable scientific research samplings, such as minerals and soil. In this work, we design and implement a jumping-flying systematic framework, enabling the jumping quadrotor to utilize hopping for movement. To achieve the jumping-flying movement, a real-time motion planning method is proposed to generate thrust-efficient jumping-flying trajectories that kinematically meet rebound characteristics. Simulation and real-world experiments show that the proposed algorithm enables the jumping quadrotor to utilize bouncing for movement, save thrust, and perform jumping flight tasks in unknown environments.