Most studies on quantum effects in the process of excitation energy transfer in photosynthesis system are based on the single-excitation initial state hypothesis, which can well describe the initial state of some photosynthesis systems that people are concerned about. But for natural and artificial photosynthesis systems that do not meet the above hypothesis, the excitation process has a non-negligible impact on the system dynamics. Based on a multi-pigments model excited by Gaussian pulse, the effects of the excitation pulse width and the excitation interval on system dynamics and excitation energy transfer efficiency are studied. First, the kinetic equations for the overall evolution of the donor system and the acceptor system that can theoretically contain any number of pigments are derived. Afterwards, the relationship between the excitation energy transfer efficiency and the related parameters of the system, as well as the optimal range of the corresponding parameters are demonstrated by numerical simulation. It is found that under the condition of donor pigments being excited by a single Gaussian pulse, there exists optimal pulse width, and the optimal range of the pigment molecule numbers, the coupling strength as well as the dephasing rate can be modulated by the pulse width. The mechanism of the above modulation is also analyzed and presented. Under the condition of donor pigments being excited by two Gaussian pulses sequentially, there exists an optimal combination of pulse width and pulse interval. The kinetic equations obtained in this paper can be extended to other forms of excitation pulses. The numerical results and the related optimal design principles obtained have reference significance for the optimal design of artificial photosynthesis systems under different light conditions.