We present mathematical expressions to compute body-wave response function for dipping anisotropic multi-layer structure. The expression is derived on the basis of ray theory incorporating reflection-transmission coefficients on velocity boundary interfaces. By using the expression, synthetic seismograms are computed for some seismic structures consisting of dipping anisotropic layers. The resultant seismograms are transformed into receiver functions. We verify that the receiver functions are approximately in agreement with those synthesized by the layer-matrix method based on wave theory. As an example, we show receiver functions calculated for an anisotropic velocity structure of the subduction zone where the oceanic plate is obliquely descending.