Compared to the voltage source inverter, the current source inverter (CSI) can boost voltage and improve filtering performance. However, the DC side of CSI is not a real current source, and the DC input current comprises a DC power supply and an inductor. In the switching process, the DC-link inductor is charged or discharged and is in an uncontrollable state. This paper proposes a novel CSI topology containing five switching tubes and a modulation strategy based on the hysteresis control strategy of the DC-link current. Due to the conduction and switching loss being positive to the DC-link current, the calculation method for the least reference value of the DC-link current is derived to meet power requirements. By constructing a virtual axis, we then present the control strategy of the output voltage in a two-phase rotating reference frame. Finally, we carry out the simulation and experiment are to validate the proposed topology, modulation, and control strategy.