Visual evoked potential (VEP)-related EEG signals have attracted widespread attention in the construction of brain-computer interface (BCI) systems. However, long-term use of the BCI system is prone to fatigue. Effectively coping with fatigue is the key to expanding BCI application scenarios. In this brief, we conduct two VEP experiments and propose a novel, concise and practical convolutional neural network (CNN) model to study and solve this problem. In detail, firstly, in terms of the stimulus frequencies in VEP experiments, we intercept the spectrum sequences of the fundamental waves and two harmonics. All these spectrum sequences are then paralleled input into the proposed multi-harmonic linkage CNN (MHLCNN) model, through three branches. Finally, the linkage characteristics of multiple harmonics are combined for VEP signal classification. The experimental results demonstrate that the proposed model shows good scalability, and can respectively improve the average classification accuracy by 23.17% and 15.85% when applied to steady-state VEP (SSVEP) signals in fatigue state and steady-state motion VEP (SSMVEP) signals, compared with the benchmark methods. All these provide a feasible and high-quality solution for reducing the impact of fatigue on the performance of VEP-based BCI systems.