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The permanent magnet synchronous generators (PMSGs), especially those with multi-phase structure, are increasingly adopted to power large-scale vehicular system with DC distribution (e.g. more electric aircraft and electric-propulsion ship). The controller design is critical in these vehicular application as they are required to maintain desired transient performance under large system disturbances. In this paper, an improved adding a power integrator (AAPI) controller is designed and adopted to regulate the six-phase active rectifier, thus enhancing the transient performance of the system. The regulation of the multi-phase active rectifier feeding large amount of dynamic instantaneous constant power load (CPL) is firstly formulated as a second-order system by utilizing a bi-linear coordinate transformation. Then, an improved AAPI finite-time controller is designed considering both asymptotic stability and the transient stability of the system. Last but not least, the effectiveness of the proposal is validated by simulation.