We address structure learning from zero-inflated count data by casting each node as a zero-inflated generalized linear model and optimizing a smooth, score-based objective under a directed acyclic graph (DAG) constraint. Our method uses node-wise likelihoods with canonical links and enforces acyclicity through a differentiable surrogate constraint combined with sparsity regularization. On simulated zero-inflated count data, it achieved superior performance with faster runtimes. In reverse engineering gene-regulatory networks (GRN), the methods demonstrated performance comparable to or better than the commonly used GRN inference baselines. The optimization is fully vectorized and mini-batched, enabling learning on larger variable sets with practical runtimes. Thus, the proposed method is competitive in learning DAG from zero-inflated count data.