An improved speech enhancement scheme is proposed based on log-spectral amplitude minimum mean-square error (LSA-MMSE) method in this paper. Burg spectrum and speech absent probability (SAP) are used to improve estimation of priori signal-to-noise ratios (SNR). The estimation of priori SNR is based on "decision-directed" criterion. Burg spectrum is introduced for noisy speech power spectrum estimation. The SAP is utilized to adjust smoothing parameter. Simulation results show that the improved estimator can well balance de-noising degree, residual musical noise and voice distortion, making enhanced voice sounds more natural.