We formulate the Schwinger-Keldysh formalism of lattice gauge theories by constructing the appropriate unitary transfer matrices in the forward and backward real-time directions for gauge- link and Wilson-Dirac fields. We can then define spectral functions at a finite lattice spacing and also formulate the linear response theory. For a real scalar field in the weak-coupling limit, the two-point Green’s function on closed time lattice path was derived analytically and the spectral function was examined numerically. The result is consistent with the continuum theory.