We investigate bulk second-order nonlinear optical properties of amorphous indium selenide thin films fabricated by thermal evaporation. Such films are shown to exhibit strong and photostable second-harmonic generation (SHG). We report strong thickness dependence of the second-harmonic signals as characterized by the Maker-fringe method. The absolute value of the nonlinear susceptibility tensor of the film is addressed by analyzing the interference of SHG signals from the film and the glass substrate. The value of the joint non-diagonal component of the susceptibility is found to be 4 pm/V, which is comparable to that of widely used second-order nonlinear materials.