Epilepsy is a common chronic brain disorder. Detecting epilepsy by observing electroencephalography (EEG) is the main method neurologists use, but this method is time-consuming. EEG signals are non-stationary, nonlinear, and often highly noisy, so it remains challenging to recognize epileptic EEG signals more accurately and automatically. This paper proposes a novel classification system of epileptic EEG signals for single-channel EEG based on the attention network that integrates time-frequency and nonlinear dynamic features. The proposed system has three novel modules. The first module constructs the Hilbert spectrum (HS) with high time-frequency resolution into a two-channel parallel convolutional network. The time-frequency features are fully extracted by complementing the high-dimensional features of the two branches. The second module constructs a grayscale recurrence plot (GRP) that contains more nonlinear dynamic features than traditional RP, fed into the residual-connected convolution module for effective learning of nonlinear dynamic features. The third module is the feature fusion module based on a self-attention mechanism to assign optimal weights to different types of features and further enhance the information extraction capability of the system. Therefore, the system is named HG-SANet. The results of several classification tasks on the Bonn EEG database and the Bern-Barcelona EEG database show that the HG-SANet can effectively capture the contribution degree of the extracted features from different domains, significantly enhance the expression ability of the model, and improve the accuracy of the recognition of epileptic EEG signals. The HG-SANet can improve the diagnosis and treatment efficiency of epilepsy and has broad application prospects in the fields of brain disease diagnosis.