EEG signals are multi-dimensional and non-stationary time series signals, and their features are not easy to extract, so large deviations are often encountered in the classification and prediction tasks. Therefore, in this paper, an EEG eye state (open or close) recognition method is proposed based on an improved convolutional neural network and the continuous wavelet transform. First, for the high noise levels encountered during EEG signal acquisition, variational mode decomposition (VMD) is used to decompose the EEG signal into several modal components, which are then subsequently used to reconstruct the signal according to the correlation principle to obtain a noiseless signal. Secondly, the continuous wavelet transform (CWT) method is used to extract the features of the EEG signals in the time and frequency domains, and the one-dimensional signal is converted into two-dimensional images to enhance the feature-learning ability convolutional networks. Finally, a residual term is introduced on the basis of the traditional convolutional neural network, and a recognition model is constructed by combining a dual channel and spatial attention mechanism. Experimental results show that the proposed model has an accuracy rate higher than 99\%, and is more effective and with better generalizability than previous studies.