The invention provides a starting method and device of a hybrid modular multilevel converter. The method comprises the steps of inputting alternating current into a plurality of full-bridge sub-modules and a plurality of half-bridge sub-modules in the converter; when the average voltage value of the plurality of full-bridge sub-modules reaches a preset threshold value, conducting a fourth switching tube in each full-bridge sub-module; when the average voltage value of the plurality of half-bridge sub-modules reaches a preset threshold value, controlling the voltage value of each full-bridge sub-module to be consistent with the voltage value of each half-bridge sub-module according to a voltage-sharing algorithm; and reducing the number of the full-bridge sub-modules and the half-bridge sub-modules input in the converter until the voltage values of the full-bridge sub-modules and the half-bridge sub-modules reach the rated voltage. According to the invention, the problem that the charging voltages of different sub-modules of the full-bridge and half-bridge hybrid modular multilevel converter are inconsistent in the AC uncontrolled charging process can be solved, the voltage consistency of the sub-modules in the starting process is ensured, and the starting failure and protection locking caused by the non-uniform capacitor voltages of different sub-modules are avoided.