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Convolutional Neural Networks (CNNs) have been regarded as the go-to models for visual recognition. More recently, convolution-free networks, based on multi-head self-attention (MSA) or multi-layer perceptrons (MLPs), become more and more popular. Nevertheless, it is not trivial when utilizing these newly-minted networks for video recognition due to the large variations and complexities in video data. In this paper, we present MLP-3D networks, a novel MLP-like 3D architecture for video recognition. Specifically, the architecture consists of MLP-3D blocks, where each block contains one MLP applied across tokens (i.e., token-mixing MLP) and one MLP applied independently to each token (i.e., channel MLP). By deriving the novel grouped time mixing (GTM) operations, we equip the basic token-mixing MLP with the ability of temporal modeling. GTM divides the input tokens into several temporal groups and linearly maps the tokens in each group with the shared projection matrix. Furthermore, we devise several variants of GTM with different grouping strategies, and compose each variant in different blocks of MLP-3D network by greedy architecture search. Without the dependence on convolutions or attention mechanisms, our MLP-3D networks achieves 68.5\%/81.4\% top-1 accuracy on Something-Something V2 and Kinetics-400 datasets, respectively. Despite with fewer computations, the results are comparable to state-of-the-art widely-used 3D CNNs and video transformers. Source code is available at https://github.com/ZhaofanQiu/MLP-3D.