Artificially designed hyperbolic metamaterial (HMM) possesses extraordinary electromagnetic features different from those of naturally existing materials. In particular, evanescent waves originally existing in vacuum can be propagating inside HMMs if hyperbolic dispersion is satisfied. This characteristic of HMMs opens a novel way to spectrally control the near-field thermal radiation in which evanescent waves play a critical role. In this paper, we theoretically investigate the performance of a near-field thermophotovoltaic (TPV) energy conversion system in which a $W/SiO_2$ -multilayer-based HMM serves as the emitter at 1000 K and InAs works as the TPV cell at 300 K. By carefully designing the thickness of constituent materials of the HMM emitter, the electric power of the near-field TPV devices can be increased by about 6 times at 100 nm vacuum gap as compared to the case of the plain W emitter. Alternatively, the HMM emitter at experimentally achievable 100 nm vacuum gap performs equivalently to the plain W emitter at 18 nm vacuum gap. We show that the enhancement mechanism of the HMM emitter is due to the coupled surface plasmon modes at multiple metal-dielectric interfaces inside the HMM emitter. With the minority career transport model, the optimal p-n junction depth of the TPV cell has also been determined at various vacuum gaps.