We theoretically investigate the high-order harmonic generation from acceptor-doped semiconductors by numerically solving the one-dimensional time-dependent Schr?dinger equation based on the single electron approximation. The results show that the harmonic efficiency of the second plateau from acceptor-doped semiconductors is about three to four orders of magnitude higher than those from undoped semiconductors. Theoretical analysis shows that doping changes the energy-band structure of the semiconductor, narrows the band gap between the valence band and the first conduction band, and between the first conduction band and the second conduction band. Then it is easier for electrons to tunnel into the higher conduction band, and the electron population of the high conduction band is increased, thus the harmonic efficiency of the second plateau is improved.