The vibrational state-selected population transfer from a highly vibrationally excited level to the ground level is of great importance in the preparation of ultra-cold molecules. By using the time-dependent quantum-wave-packet method, the population transfer dynamics is investigated theoretically for the HF molecule. A double-∑-type laser scheme is proposed to transfer the population from the ∣v=16〉 level to the ground vibrational level ∣v=0〉 on the ground electronic state. The scheme consists of two steps: The first step is to transfer the population from ∣v=16〉 to ∣v=7〉 via an intermediate level ∣v=11〉, and the second one is to transfer the population from ∣v=7〉 to ∣v=0〉 via ∣v=3〉. In each step, three vibrational levels form a ∑-type population transfer path under the action of two temporally overlapped laser pulses. The maximal population-transfer efficiency is obtained by optimizing the laser intensities, frequencies, and relative delays. Cases for the pulses in intuitive and counterintuitive sequences are both calculated and compared. It is found that for both cases the population can be efficiently (over 90%) transferred from the ∣v=16〉 level to the ∣v=0〉 level.