In this paper, we present an investigation about scattering analysis of an transmission boundary value problem (TBVP) which consists a discrete Schrödinger equation and transmission conditions. Discussing the Jost solution and scattering function of this problem, we find the properties of scattering function of this problem by using the scattering solutions. We also investigate the discrete spectrum of this boundary value problem. Furthermore, we apply the results on an example which is the special case of main TBVP and we discuss the existence of eigenvalues of this example.