The mediation analysis methodology of the cause-and-effect relationship through mediators has been increasingly popular over the past decades. The human microbiome can contribute to the pathogenesis of many complex diseases by mediating disease-leading causal pathways. However, standard mediation analysis is not adequate for microbiome data due to the excessive number of zero values and the over-dispersion in the sequencing reads, which arise for both biological and sampling reasons. To address these unique challenges brought by the zero-inflated mediator, we developed a novel mediation analysis algorithm under the potential-outcome framework to fill this gap. The proposed semiparametric model estimates the mediation effect of the microbiome by decomposing indirect effects into two components according to the zero-inflated distributions. The bootstrap algorithm is utilized to calculate the empirical confidence intervals of the causal effects. We conducted extensive simulation studies to investigate the performance of the proposed weighting-based approach and some model-based alternatives, and our proposed model showed robust performance. The proposed algorithm was implemented in a real human microbiome study of identifying whether some taxa mediate the relationship between LACTIN-V treatment and immune response.