This paper employs the wavelet-Galerkin time domain (WGTD) technique to study composite scattering of arbitrarily target and a lossy ground, and the incidence is realized through three-wave technology. The far-field radiated by the surface currents is calculated using the reciprocity theorem instead of the more complicated Sommerfeld integration. Numerical radar cross section demonstrate the validity and precision of WGTD. Compared to finite difference time domain method, the WGTD method has the advantages of smaller memory and higher efficiency.