Simplicial complexes have recently been in the limelight of higher-order network analysis, where a minority of simplices play crucial roles in structures and functions due to network heterogeneity. However, it remains elusive how to characterize simplices’ influence and identify vital simplices of order p (termed p-simplices), despite the relative maturity of research on vital nodes (0-simplices) identification. Meanwhile, graph neural networks (GNNs) are potent tools that can exploit network topology and node features simultaneously, but they struggle to tackle higher-order tasks. In this paper, powered by GNN techniques, we propose hierarchical simplicial convolutional networks (HiSCN) to identify vital p-simplices incorporating real influence scores derived from samples or propagation simulations. It can tackle higher-order tasks by leveraging novel higher-order presentations: hierarchical bipartite graphs and higher-order hierarchical (HoH) Laplacians, where targeted simplices are grouped into a hub set and can interact with other simplices. Besides, HiSCN employs learnable graph convolutional operators in each HoH Laplacian domain to capture interactions among simplices, and it can identify influential simplices of arbitrary order by changing the hub set. Empirical results demonstrate that HiSCN significantly outperforms existing methods in ranking both 0-simplices (nodes) and 2-simplices. In general, this novel framework excels in identifying influential simplices and promises to serve as a potent tool in higher-order network analysis.