There are multiple converter stations in a multi-terminal voltage source converter-high voltage direct current(VSC-HVDC )transmission system, and the complex coupling relationship among converter stations makes the calculation of DC short-circuit current a challenge. For the scenarios of a multi-terminal VSC-HVDC transmission system containing hybrid modular multi-level converter（MMC）, firstly the fault equivalent model of the hybrid MMC before and after DC fault ride-through is established, and the influence of DC fault ride-through on the short-circuit current of the multi-terminal VSC-HVDC transmission system is analyzed from the perspective of the change in circuit structure during DC fault ride-through of a hybrid MMC. Based on the superposition theorem, the concept of DC fault ride-through additional network is proposed. Then, a short-circuit current calculation method of the multi-terminal system containing hybrid MMC is proposed during DC fault ride-through, combining the approximate decoupling analytic calculation method of multi-terminal system and the concept of DC fault ride-through additional network. Finally, the electromagnetic transient simulation results based on PSCAD/EMTDC show that the maximum error of the short-circuit current values calculated within 6 ms of the fault occurrence is within ±6%, and the proposed calculation method has good applicability. It provides a reference for the planning, design, and protection setting of multi-terminal VSC-HVDC transmission systems containing hybrid MMC.