We propose a new model to address the overlooked problem of node clustering in simple hypergraphs. Simple hypergraphs are suitable when a node may not appear multiple times in the same hyperedge, such as in co-authorship datasets. Our model assumes the existence of latent node groups and hyperedges are conditionally independent given these groups. We first establish the generic identifiability of the model parameters. We then develop a variational approximation Expectation-Maximization algorithm for parameter inference and node clustering, and derive a statistical criterion for model selection. To illustrate the performance of our R package HyperSBM, we compare it with other node clustering methods using synthetic data generated from the model, as well as from a line clustering experiment and a co-authorship dataset. As a by-product, our synthetic experiments demonstrate that the detectability thresholds for non-uniform sparse hypergraphs cannot be deduced from the uniform case.