By using the time-dependent multilevel approach, we have calculated the coherent population transfer among the quantum states of potassium atom by a single frequency-chirped laser pulse. The results show that the population can be efficiently transferred to a target state and be trapped there by using an ‘intuitive’ or a ‘counter-intuitive’ frequency sweep laser pulse in the case of ‘narrowband’ frequency-chirped laser pulse. It is also found that a pair of sequential ‘broadband’ frequency-chirped laser pulses can efficiently transfer population from one ground state of the A atom to the other one.