We propose a video denoising algorithm based on a spatiotemporal Gaussian scale mixture (ST-GSM) model in the wavelet transform domain. This model simultaneously captures local correlations between the wavelet coefficients of natural video sequences across both space and time. Bayes least square estimation is used to recover the original signal from the noisy observation. To further improve the performance, motion compensation is employed before ST-GSM denoising, where a Fourier domain noise-robust cross correlation approach is proposed for motion estimation. Experiments show that the performance of the proposed method is highly competitive when compared with state-of-the-art video denoising algorithms.