A model of the thermophotovoltaic device combining a near-field thermal emitter and a hot-carrier solar cell is established. The fluctuating electromagnetic near-field theory for the radiative thermal transport and Landauer's formula for the carrier extraction are introduced. Expressions for the efficiency and the power output of the device are derived. How the voltage and the extraction energy of the energy selective contacts affect the performance of the device is revealed. The results show that the efficiency of the proposed device can be greatly enhanced by exploiting the radiation between the emitter and the cell and extracting carriers through electron tunneling effects.