Simulation of modular multilevel converter (MMC) based high-voltage direct current (HVDC) systems assumes significance due to their growing popularity. It could assist with the design of hardware, control systems of MMC and HVDC networks, and power system topology. However, simulation of MMC-HVDC using existing software takes a long time due to the presence of a large number of states and non-linear devices. This paper presents an ultra-fast single- or multi-CPU simulation algorithm to simulate the MMC-HVDC system based on state-space models and using hybrid discretization algorithm with a relaxation technique that reduces the imposed computational burden. Using the developed simulation algorithm, a control system is developed for an MMC-HVDC system that reduces the switching losses in the system.