This paper proposes a novel evaluation method for the risk of simultaneous commutation-failures (CFs) in multi-infeed high-voltage direct-current (HVDC) systems, which takes into account the DC current rise caused by the inverter AC system fault. By calculating a multi-infeed interaction factor (MIIF), and using an equivalent model for multi-infeed HVDC systems. The effect of DC-current on commutation failure is analyzed and the factors that affect the simultaneous commutation-failure are determined. Based on the equivalent equation for both the DC line and DC control, a time-domain expression for the DC-current caused by the inverter AC system fault is calculated. Based on this, this paper describes a novel CF evaluation method that takes into account DC current rise by solving for the maximum of the DC current. Several useful parameters like the MIIF, the critical multi-infeed commutation failure factor (CMICFF), and the multi-infeed commutation failure factor (MICFF) are defined, and a method for the risk of simultaneous commutation-failure in multi-infeed HVDC systems by comparing CMICFF and MICFF is proposed. The accuracy of the method proposed in this paper is validated by a comparison with a simulation using the software PSCAD/EMTDC.