This study proposes a hybrid electromechanical and electro-magnetic transient (EMT) simulation algorithm, which interfaces the EMT-type modular multilevel converter (MMC) high-voltage direction current (HVDC) model into transient stability simulation. The proposed hybrid simulation algorithm offers high fidelity simulation results for the fast transient phenomenon of the MMC HVDC using the EMT program (EMTP). At the same time, the hybrid simulation algorithm utilises the transient stability program (TSP) to represent a large external AC network connected to the MMC HVDC. Thus, the proposed hybrid simulator combines the advantages of the TSP and EMTP simulations and offers accurate and efficient solutions for the integrated AC and HVDC systems. A case study of MMC HVDC system connected to 10-generator 39-bus New England AC System is simulated using hybrid and full-EMTP simulations in PSCAD/EMTDC. The simulation results demonstrate the proposed hybrid simulator produces accurate simulation results compared to the full-EMTP solutions.