Abstract Population transfer between the fine structure levels of the cesium atom is numerically investigated when a linearly chirped Gaussian pulse interacts with the atom. For this purpose, the time-dependent Hamiltonian of the quantum system is developed and the Schrodinger equation is solved. In result the transition probabilities are obtained and discussed towards precise controlling of the system dynamics. The results show that for both single-pulse and multi-pulse cases, the probability of the final population distribution of levels can be flexibly controlled by optimal adjustment of the laser parameters. In addition, it is shown that the transition probabilities increase with the increasing of the pulse duration in the single pulse case as well as increasing the number of pulses in the multi-pulse system.