The channel estimation method for millimeter-wave communication includes virtual multipath acquisition and sparse reconstruction. In the virtual multipath acquisition stage, instead of searching the real multipath components (MPCs), the virtual representation of the real MPCs is derived, and the hierarchical search is utilized to acquire the virtual MPCs based on a normal limited-resolution codebook. In the sparse reconstruction stage, the real MPCs are reconstructed from the virtual MPCs acquired in the virtual multipath acquisition stage. An enhanced sub-array scheme is used to design a hierarchical codebook under a strict constant-modulus constraint. The designed codebook can be used for both analog and hybrid beamforming/combining devices. The training overhead of channel estimation and the complexity of the search are significantly reduced, and the size of the dictionary matrix is greatly reduced by exploiting the results of the virtual multipath acquisition.