Independent Component Analysis (ICA) is a multivariate data analysis tool. The basic principle of ICA is the assumption of independency of the source data. On the separation of the data source, ICA algorithm searches for a demixing matrix that will maximize the independency. This searching process is mostly done in iterative way and involving high order statistics. This process is time consuming. For a certain application, such as speech, where the source signal has its power at the lower frequency, we can reduce the data length by removing the high frequency component. Wavelet decomposition is a popular method for this purpose. In this paper, we propose the data reduction using Wavelet as a preprocessing of ICA to speed up the ICA computation. We investigate Haar, Daubechies 2, Daubechies 3, and Daubechies 4 Wavelet as the wavelet analysis. We further investigate the computation time as the function of level of decomposition of the wavelet. In this study, we found that Haar Wavelet at third level of decomposition gave the biggest advantage of computation speed, which is about 40-50%.