We have developed a tailless, two-winged flapping drone with a full span length of 180 mm and a total weight of 20.5 g. The developed flapping drone is characterized by three biomimetic techniques: an anisotropic vein pattern reinforcing the wing surfaces, an elastic flapping mechanism, and gravity center position control in the abdomen. On the basis of experimental and numerical results, the flapping wings are reinforced by a vein pattern made of an anisotropic carbon fiber-reinforced plastic (CFRP) laminate to passively provide appropriate aeroelastic deformation and positively utilize snap-though buckling on the wing surface at stroke reversals to provide a fast feathering rotation. The flapping wing kinematics are provided by a novel flapping mechanism with an energy recovery system using the elasticity of the mechanical system. Unlike other previously developed flapping robots, feedback control to stabilize the pitch and roll angles of the drone’s body is conducted using a technique of gravity center position control, where the tail angles of the body are changed similarly to the abdominal movements of insects in flight. The developed flapping drone has succeeded in an autonomous hovering flight for more than 30 s and a vertical take-off under a wireless condition with the gravity center position control.