Graphical models are a popular approach to find dependence and conditional independence relationships between gene expressions. Directed acyclic graphs (DAGs) are a special class of directed graphical models, where all the edges are directed edges and contain no directed cycles. The DAGs are well known models for discovering causal relationships between genes in gene regulatory networks. However, estimating DAGs without assuming known ordering is challenging due to high dimensionality, the acyclic constraints, and the presence of equivalence class from observational data. To overcome these challenges, we propose a two-stage adaptive Lasso approach, called NS-DIST, which performs neighborhood selection (NS) in stage 1, and then estimates DAGs by the Discrete Improving Search with Tabu (DIST) algorithm within the selected neighborhood. Simulation studies are presented to demonstrate the effectiveness of the method and its computational efficiency. Two real data examples are used to demonstrate the practical usage of our method for gene regulatory network inference.