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Using the time-dependent multilevel approach, we have calculated the coherent population transfer between the quantum states of potassium atom by a single frequency-chirped laser pulse. The result shows that a pair of sequential ’broadband’ frequency-chirped laser pulses can efficiently transfer population from the initial state of the ladder system to the target state. It is also found that the population can be efficiently transferred to a target state and trapped there by using an ’intuitive’ or a ’counterintuitive’ frequency sweep laser pulse in the case of ’narrowband’ frequency-chirped laser pulse. Our research shows that the complete population transfer is related to the pulse duration, chirp rate, and amplitude of the laser pulse.