Graph classification is an important problem with applications across many domains, for which the graph neural networks (GNNs) have been state-of-the-art (SOTA) methods. In the literature, to adopt GNNs for the graph classification task, there are two groups of methods: global pooling and hierarchical pooling. The global pooling methods obtain the graph representation vectors by globally pooling all the node embeddings together at the end of several GNN layers, while the hierarchical pooling methods provide one extra pooling operation between the GNN layers to extract the hierarchical information and improve the graph representations. Both global and hierarchical pooling methods are effective in different scenarios. Due to highly diverse applications, it is challenging to design data-specific pooling methods with human expertise. To address this problem, we propose PAS (Pooling Architecture Search) to design adaptive pooling architectures by using the neural architecture search (NAS). To enable the search space design, we propose a unified pooling framework consisting of four modules: Aggregation, Pooling, Readout, and Merge. Two variants PAS-G and PAS-NE are provided to design the pooling operations in different scales. A set of candidate operations are designed in the search space on top of this framework, and then existing human-designed pooling methods, including global and hierarchical ones, can be incorporated. To enable efficient search, a coarsening strategy is developed to continuously relax the search space, and then a differentiable search method can be adopted. We conduct extensive experiments on six real-world datasets, including the large-scale datasets MR and ogbg-molhiv. Experimental results in this paper demonstrate the effectiveness and efficiency of the proposed PAS in designing the pooling architectures for graph classification. Besides, the Top-1 performance on two Open Graph Benchmark (OGB) datasets further indicates the utility of PAS when facing diverse realistic data. The implementation of PAS is available at: https://github.com/AutoML-Research/PAS.