Dense spatial sampling (~1m) and low signal-to-noise ratio (SNR) are typical features of distributed acoustic sensing (DAS) data. We have developed a wavelet stacking method to attenuate DAS noise without compromising data bandwidth. Wavelet stack consists of two steps, adaptive nonlinear iterative denoise and nonlinear stack. Nonlinear iterative filtering is based on combination of 1D stationary wavelet transform, 2D complex wavelet transform (CWT) and normal moveout. It is non-stationary and adaptive to noise variation. Nonlinear stack combines two denoised gathers in the CWT domain in a predictable way for further SNR uplift without loss of the high frequency information of either input. Wavelet stack is used to produce partially stacked DAS channel gathers. Significant seismic resolution uplift in field DAS data is demonstrated using the newly developed wavelet stack compared to a conventional linear stack.