In this paper, we present an optimal shape design method for a dielectric microlens which is used to focus an incoming infrared plane wave in wideband, by exploiting the finite difference time domain (FDTD) technique and the topology optimization technique. Topology optimization is a scheme to search an optimal shape by adjusting the material properties, which are design variables, within the design space. And by introducing the adjoint variable method, we can effectively calculate a derivative of the objective function with respect to the design variable. To verify the proposed method, a shape design problem of a dielectric microlens is tested when illuminated by a transverse electric (TE)-polarized infrared plane wave. In this problem, the design variable is the dielectric constant within the design space of a dielectric microlens. The design objective is to maximally focus the incoming magnetic field at a specific point in wideband.