In this paper, we propose a simple slider-crank mechanism using flexible links, which realizes both a wide flapping angle and lead-lag motion for a small flapping robot. Butterfly-style flight is promising because of its low flapping frequency and few degrees of freedom, unlike the flights of flies and dragonflies. However, since a butterfly flaps its wings over 140 deg and claps both left and right wings, a conventional slider-crank mechanism cannot generate sufficient torque for flapping at the top dead point where the driver and follower are parallel. Moreover, the addition of an actuator for lead-lag motion makes the system heavy and complex. To overcome these problems, we developed a new slider-crank mechanism that can flap the wings widely by bending the flexible links and that realizes the lead-lag motion by twisting them. The proposed mechanism improved the flight performance of a butterfly-style flapping robot by 20 % compared with the model without lead-lag motion.