The photon transport and energy conversion of a near-field thermophotovoltaic (TPV) system with a selective emitter composed of alternate tungsten and alumina layers and a photovoltaic cell sandwiched by electrical contacts are theoretically investigated in this paper. Fluctuational electrodynamics along with the dyadic Green's function for a multilayered structure is applied to calculate the spectral heat flux, and the photocurrent generation and electrical power output are solved from the photon-coupled charge transport equations. The tungsten and alumina layer thicknesses are optimized to obtain maximum electrical power output for bare TPV cell. The spectral heat flux is much enhanced when plain tungsten emitter is replaced with the multilayer emitter due to the effective medium intrinsic lossy property and additional surface plasmon polariton coupling in the tungsten thin film, for which the invalidity of effective medium theory to predict photon transport in the near field with multilayer emitters is discussed. Effects of a gold back reflector and indium tin oxide front coating with nanometer thickness, which could practically act as the electrodes to collect the photon-generated charges on the TPV cell, are explored. The conversion efficiency of 23.7% and electrical power output of 0.31 MW/m2 can be achieved at a vacuum gap distance of 100 nm when the emitter and receiver temperature are, respectively, set as 2000 K and 300 K.