The quality of narrowband speech can be enhanced by the bandwidth extension technology. This paper proposes a mixed excitation and an energy compensation method based on Gaussian Mixture Model (GMM). First, we employ the mixed excitation model having both periodic and aperiodic characteristics in frequency domain. We use a filter bank to extract the periodicity features from the filtered signals and model them based on GMM to estimate the mixed excitation. Second, we separate the acoustic space into the voiced and unvoiced parts of speech to compensate for the energy difference between narrowband speech and reconstructed highband, or lowband speech, more accurately. Objective and subjective evaluations show that the quality of wideband speech reconstructed by the proposed method is superior to that by the conventional bandwidth extension method.