Tidal energy is one of the key components in increasing the penetration of renewable energy. High tidal energy penetration into the electrical grid depends on accurate tidal current speed forecasting. Model inaccuracies hinder forecast accuracy. Previous research primarily used physical models to forecast tidal current speed, yet tidal current variations influenced by the orbital periods of celestial bodies make accurate physical modeling challenging. Research on the multi-periodicity of tides is crucial for forecasting tidal current speed. We propose the Wavelet-Enhanced Convolutional Network to learn multi-periodicity. The framework embeds intra-period and inter-period variations of one-dimensional tidal current data into the rows and columns, respectively, of a two-dimensional tensor. Then, the two-dimensional variations of the sequence can be processed by convolutional kernels. We integrate a time-frequency analysis method into the framework to further address local periodic features. Additionally, to enhance the framework's stability, we optimize the framework's hyperparameters with the Tree-structured Parzen Estimator. The proposed framework captures multi-periodic dependencies in tidal current data. Numerical results show a 10-step average Mean Absolute Error of 0.025, with at least a 1.44% error reduction compared to other baselines. Further ablation studies show a 1.4% reduction in Mean Absolute Percentage Error on the data with artificially added periodic fluctuations.