In this paper, a two-stage dual tree complex wavelet packet transform (DTCWPT) based speech enhancement algorithm has been proposed, in which a speech presence probability (SPP) estimator and a generalized minimum mean squared error (MMSE) estimator are developed. To overcome the drawback of signal distortions caused by down sampling of WPT, a two-stage analytic decomposition concatenating undecimated WPT (UWPT) and decimated WPT is employed. An SPP estimator in the DTCWPT domain is derived based on a generalized Gamma distribution of speech, and Gaussian noise assumption. The validation results show that the proposed algorithm can obtain enhanced perceptual evaluation of speech quality (PESQ), and segmental signal-to-noise ratio (SegSNR) at low SNR nonstationary noise, compared with other four state-of-the-art speech enhancement algorithms, including optimally modified LSA (OM-LSA), soft masking using a posteriori SNR uncertainty (SMPO), a posteriori SPP based MMSE estimation (MMSE-SPP), and adaptive Bayesian wavelet thresholding (BWT).