Semi-continuous data have a point mass at zero and are continuous with positive support. Such data arise naturally in several real-life situations like signals in a blind source separation problem, daily rainfall at a location, sales of durable goods among many others. Therefore, efficient estimation of the underlying probability density function is of significant interest. In this paper, we present an estimation method for semi-continuous data based on the maximum entropy principle and demonstrate its successful application in developing an Independent Component Analysis (ICA) algorithm, ICASemi- continuous Entropy Maximization, (ICA-SCEM). We present a theoretical analysis of the proposed estimation technique and using simulated data we demonstrate the superior performance of ICA-SCEM over classical ICA algorithms.