In this paper, we propose a high-precision digital framework to compensate for non-ideal effects in the analog front-end circuits for wireless communication systems. The IQ imbalance and the carrier frequency offset (CFO) are jointly estimated with a band-selective mechanism of the orthogonal frequency division multiplexing (OFDM) system. The compensable CFO range is four times wider than prior schemes. The proposed mechanism divides the whole range of CFO bandwidth into three bands: the high-CFO band, the medium-CFO band, and the low-CFO band. The least-square (LS) based method is performed to simultaneously estimate the IQ imbalance and the CFO. Simulation results show that the proposed band-selective algorithm provides accurate estimation, with the average error less than 0.13%.