Belavin's Z(n)-symmetric elliptic model with boundary reflection is considered on the basis of the boundary CTM bootstrap. We find non-diagonal K-matrices for n > 2 that satisfy the reflection equation (boundary Yang-Baxter equation), and also find non-diagonal Boltzmann weights for the A(n-1)((1))-face model even for n greater than or equal to 2. We derive difference equations of the quantum Knizhnik-Zamolodchikov type for correlation functions of the boundary model. The boundary spontaneous polarization is obtained by solving the simplest difference equations in the case of the free boundary condition. The resulting quantity is the square of the spontaneous polarization for the bulk Z(n)-symmetric model, up to a phase factor.