The flapping flight of tiny insects such as flies or larger insects such as butterflies is of fundamental interest not only in biology itself but also in its practical use for the development of micro air vehicles (MAVs). It is known that a butterfly flaps downward for generating the lift force and backward for generating the thrust force. In this study, we consider a simple butterfly-like flapping wing–body model in which the body is a thin rod and the rectangular rigid wings flap in a simple motion. We investigate lift and thrust generation of the model by using the immersed boundary–lattice Boltzmann method. First, we compute the lift and thrust forces when the body of the model is fixed for Reynolds numbers in the range of 50–1000. In addition, we estimate the supportable mass for each Reynolds number from the computed lift force. Second, we simulate free flights when the body can only move translationally. It is found that the expected supportable mass can be supported even in the free flight except when the mass of the body relative to the mass of the fluid is too small, and the wing–body model with the mass of actual insects can go upward against the gravity. Finally, we simulate free flights when the body can move translationally and rotationally. It is found that the body has a large pitch motion and consequently gets off-balance. Then, we discuss a way to control the pitching angle by flexing the body of the wing–body model.