The model of a near-field solar thermophotovoltaic system (NF-STPVS) consisting of a solar concentrator, an absorber, an emitter, an optical filter, and a photovoltaic (PV) cell is proposed, in which the near-field radiation between the emitter and the PV cell, the radiation and reflection losses from the absorber to the environment, and the finite-rate heat transfer between the PV cell and the heat sink are taken into account. By using the fluctuational electrodynamics and irreversible thermodynamics, formulas for the power output and efficiency of the system are analytically derived. By solving energy balance equations, the operating temperatures of the emitter and the PV cell are calculated for given values of the output voltage of the PV cell and the vacuum gap. The concentration factor at the maximum efficiency of the system is optimally given. Furthermore, the maximum efficiencies of the system are calculated for two cases of the absence and presence of the Auger recombination and the corresponding optimum values of several key parameters are determined.