Community search has been extensively studied in the past decades. In recent years, there is a growing interest in attributed community search that aims to identify a community based on both the query nodes and query attributes. A set of techniques have been investigated. Though the recent methods based on advanced learning models such as graph neural networks (GNNs) can achieve state-of-the-art performance in terms of accuracy, we notice that 1) they suffer from severe efficiency issues; 2) they directly model community search as a node classification problem and thus cannot make good use of interdependence among different entities in the graph. Motivated by these, in this paper, we propose a new neurAL attrIbuted Community sEarch model for large-scale graphs, termed ALICE. ALICE first extracts a candidate subgraph to reduce the search scope and subsequently predicts the community by the Consistency-aware Net , termed ConNet. Specifically, in the extraction phase, we introduce the density sketch modularity that uses a unified form to combine the strengths of two existing powerful modularities, i.e., classical modularity and density modularity. Based on the new modularity metric, we first adaptively obtain the candidate subgraph, formed by the k-hop neighbors of the query nodes, with the maximum modularity. Then, we construct a node-attribute bipartite graph to take attributes into consideration. After that, ConNet adopts a cross-attention encoder to encode the interaction between the query and the graph. The training of the model is guided by the structure-attribute consistency and the local consistency to achieve better performance. Extensive experiments over 11 real-world datasets including one billion-scale graph demonstrate the superiority of ALICE in terms of accuracy, efficiency, and scalability.