||Selecting a highly-connected subgraph from a hypergraph, analogous to k-core in the ordinary graph with pairwise interactions, is an essential subject in network science society. Here, we consider (k,q)-core percolation in hypergraphs. The (k,q)-core is the largest subgraph in which vertices have at least k hypergraph degree, and hyperedges contain at least q vertices. To obtain the dynamic equation for (k,q)-core and the percolation threshold, we construct an analytic framework to understand the transition behavior. We find that a hybrid transition occurs for either k>2 or q>2 at a finite transition point. We also quantify the critical slowing down that appears at this critical point.