Sequencing-based technologies provide an abundance of high-dimensional biological datasets with skewed and zero-inflated measurements. Classification of such data with linear discriminant analysis leads to poor performance due to the violation of the Gaussian distribution assumption. To address this limitation, we propose a new semiparametric discriminant analysis framework based on the truncated latent Gaussian copula model that accommodates both skewness and zero inflation. By applying sparsity regularization, we demonstrate that the proposed method leads to the consistent estimation of classification direction in high-dimensional settings. On simulated data, the proposed method shows superior performance compared to the existing method. We apply the method to discriminate healthy controls from patients with Crohn’s disease based on microbiome data and to identify genera with the most influence on the classification rule.