Considering dynamics of a pulse-driven finite-dimensional quantum system with near degenerate eigenstates, the multi-level system model includes one ground state and a number of excited states, in which the transitions exist between the ground state and any excited state. Population transfer induced by different kinds of pulses in this multi-level system were investigated. It is noted that in the case of both weak and strong fields, the quantum system can be reduced to a two-level system. Analytical relations between the original system and the reduced system are obtained for weak fields with multi frequencies and strong fields with one frequency. These results can be generalized to a multi-level system with several sets of near-degenerated eigenstates, and the conclusion can be utilized to identify the effective dimension of a quantum multi-level system controlled by laser.