For a mesoscopic hybrid system which contains a normal central region coupled to multiple superconducting leads, a general expression of the current is derived by using nonequilibrium-Green-function method. This current formula can be used to describe the case with time-dependent external fields applied to any parts of the system, arbitrarily finite voltages, and any kinds of interactions in the central region. For a normal two-terminal interacting electron system, this expression reduces to the general time-dependent current formula previously obtained by Wingreen et al. [Phys. Rev. B 98, 8487 (1993)]. As an application, we use this current formula to study a special case of a noninteracting single-level central region coupled to two or three superconducting leads, respectively.published_or_final_versio
