Objective. Steady-state visual evoked potential (SSVEP)-based brain-computer interfaces (BCIs) can provide relatively easy, reliable and high speed communication. However, the performance is still not satisfactory, especially in some users who are not able to generate strong enough SSVEP signals. This work aims to strengthen a user's SSVEP by alpha down-regulating neurofeedback training (NFT) and consequently improve the performance of the user in using SSVEP-based BCIs. Approach. An experiment with two steps was designed and conducted. The first step was to investigate the relationship between the resting alpha activity and the SSVEP-based BCI performance, in order to determine the training parameter for the NFT. Then in the second step, half of the subjects with 'low' performance (i.e. BCI classification accuracy <80%) were randomly assigned to a NFT group to perform a real-time NFT, and the rest half to a non-NFT control group for comparison. Main results. The first step revealed a significant negative correlation between the BCI performance and the individual alpha band (IAB) amplitudes in the eyes-open resting condition in a total of 33 subjects. In the second step, it was found that during the IAB down-regulating NFT, on average the subjects were able to successfully decrease their IAB amplitude over training sessions. More importantly, the NFT group showed an average increase of 16.5% in the SSVEP signal SNR (signal-to-noise ratio) and an average increase of 20.3% in the BCI classification accuracy, which was significant compared to the non-NFT control group. Significance. These findings indicate that the alpha down-regulating NFT can be used to improve the SSVEP signal quality and the subjects' performance in using SSVEP-based BCIs. It could be helpful to the SSVEP related studies and would contribute to more effective SSVEP-based BCI applications.