The performance of a near-field thermophotovoltaic system with a tandem-cell structure composed of thin-film p-doped GaSb and n-doped InAs sub-cells on a gold backside reflector is theoretically investigated. The temperatures of the Ga-doped ZnO emitter and the tandem cells are set as 1800 K and 300 K, while the thicknesses of GaSb and InAs sub-cells are considered as 15 m and 0.5 μm, respectively. Fluctuational electrodynamics along with the multilayer dyadic Green’s function is used to study near-field radiative heat transfer with the consideration of photon chemical potential, whereas radiative recombination and nonradiative Auger recombination are taken into account for evaluating the electrical performance of the tandem cells. At a vacuum gap of 50 nm, it is found that the tandem cells with independent charge collections achieve electrical power output 468.8 kW/m2 at a conversion efficiency of 41%, generating relatively 87% (or 21%) more power with about absolute 5% (or 10%) higher efficiency than the single GaSb (or InAs) cell of the same 2-μm thickness. The physical mechanism of near-field spectral heat transfer is elucidated with energy transmission coefficient, while the current-voltage characteristics of sub-cells are discussed in detail. This work will pave the way to enhance near-field thermophotovoltaic energy conversion performance with tandem or multi-junction cells.