Thermophotovoltaic (TPV) device is a thermoelectric conversion method with great application prospects. In the far-field regime, the thermoelectric power is usually small due to the Planck blackbody radiation limit, but can be substantially enhanced in the near-field regime where evanescent waves will participate in the heat transfer by tunneling. In this aspect, the surface optical density of state is a key factor that will determine the transfer conversion of thermal photons. Plasmonic or phononic resonance materials have been discussed in the literature to acquire large heat flux. Besides, metamaterial is another way to pursue the design freedoms for the same purpose. In this work, we propose a CaF₂/W_n multilayer based infrared hyperbolic metamaterial (HMM) with high surface density of states as an emitter of a high-performance TPV cell made of an InSb p-n junction (energy bandgap = 0.17 eV). The effective medium theory (EMT) is utilized to describe the electromagnetic behavior of the HMM. The near-field heat flux is calculated based on electrodynamic wave theory and Green's function method, and the photocurrent of thermophotovoltaic device is derived using diffusion equation for semiconductor. For comparison, we design three different radiators, i.e. tungsten film (W), GaF₂/W_n multilayer hyperbolic metamaterial (HMM), and tungsten-grounded HMM (WHMM). Compared with the pure tungsten radiator, the artificial structure exhibits the hyperbolic dispersion characteristic in a wide frequency range, which gives rise to a higher local density of states, in particular in the hyperbolic-to-elliptic spectral transition region. As a result, the radiation power and the energy conversion efficiency are greatly enhanced, which are more easily realized by a matched emission band achieved by the structural design. We find that the thermophotovoltaic device with WHMM radiator has a similar power and conversion efficiency to that with the HMM radiator. The influence of the substrate can be ignored when the hyperbolic metamaterial is thicker than 140 nm, very beneficial to the actual fabrication of the device. By our system, with multilayer hyperbolic metamaterial (HMM) radiator, a high electric power >1 W/m² and a conversion efficiency about 11% can be obtained at a bias temperature of 200 K and a 100 nm vacuum gap. Compared with nanowire arrays or natural hyperbolic material, the multilayer structure proposed in this paper has obvious advantages in bandwidth and manufacturing and may find important applications in near-field thermophotovoltaic device and other relevant areas.