Low-temperature photoluminescence spectra of n-InSe layered single crystals were studied in the temperature range 10-210 K. Photoluminescence of n-InSe showed peaks at 1.334, 1.306, 1.288, and 1.232 eV at 10 K. These four peaks were attributed to radiative recombination of the direct free excitons, an impurity-band transition, a donor-acceptor recombination channel, and the transition within an impurity-vacancy complex, respectively. To determine the temperature dependence of direct band gap of n-InSe, we estimated the exciton binding energy to be 15 meV by assuming an isotropic approximation for the anisotropy parameter gamma = 1. From these peak positions and the estimated band gap, the donor and acceptor levels associated with these centers were estimated to be approximately 43 and 18 meV, respectively. The temperature variations of the peak energy and linewidth of the excitons in n-InSe were explained by taking into account both the exciton-acoustic-phonon and the exciton-optical-phonon interactions. Below approximate to 60 K, these variations are due mainly to exciton scattering by acoustic phonons via the deformation potential in InSe.