Electromagnetic transient (EMT) simulations are often performed to analyze disturbances which occur during a steady-state operation of the power grid. In modern transmission and distribution power grids, a number of voltage-source converters (VSCs) are used for renewable energy interconnections and system control. To perform EMT simulations with such VSCs, a time step of the order of microseconds is used to represent the switching operations of the VSCs. In order to avoid a prohibitively-long computation time, a steady-state initialization method is required to directly start from a steady state. This paper proposes a systematic and heuristic procedure for the steady-state initialization of generic VSCs. Using an AC steady-state solution, detailed portions in the circuit part and the control-system part of a VSC are systematically initialized. For validation, EMT simulations of a 6.6-kV distribution grid with two VSCs are performed with and without the proposed initialization procedure in this paper. Practically no transient is observed in the result with the proposed procedure, and therefore it is confirmed that directly starting from a steady state is made possible. On the other hand, the result without the proposed procedure does not reach the steady state even after continuing the EMT simulation for 300 ms.