Due to the limitations in the accuracy and robustness of current electroencephalogram (EEG) classification algorithms, applying motor imagery (MI) for practical Brain-Computer Interface (BCI) applications remains challenging. This paper proposed a model that combined a three-dimensional convolutional neural network (CNN) with a long short-term memory (LSTM) network with attention to classify MI-EEG signals. This model combined MI-EEG signals from different channels into three-dimensional features and extracted spatial features through convolution operations with multiple three-dimensional convolutional kernels of different scales. At the same time, to ensure the integrity of the extracted MI-EEG signal temporal features, the LSTM network was directly trained on the preprocessed raw signal. Finally, the features obtained from these two networks were combined and used for classification. Experimental results showed that this model achieved a classification accuracy of 92.7% and an F1-score of 0.91 on the public dataset BCI Competition IV dataset 2a, which were both higher than the state-of-the-art models in the field of MI tasks. Additionally, 12 participants were invited to complete a four-class MI task in our lab, and experiments on the collected dataset showed that the 3D-CLMI model also maintained the highest classification accuracy and F1-score. The model greatly improved the classification accuracy of users' motor imagery intentions, giving brain-computer interfaces better application prospects in emerging fields such as autonomous vehicles and medical rehabilitation.