Steady-state visual evoked potentials (SSVEPs) have garnered significant attention from researchers due to their utility in brain-computer interface (BCI) systems. In this context, the generation of synthetic SSVEP signals with controllable features, such as a specified signal-to-noise ratio (SNR), provides a valuable tool for the precise analysis of these signals and the development of novel processing methods. In this study, a method for generating synthetic SSVEP signals with a predefined SNR based on the power law is proposed. To achieve this, the power spectrum of the artificial signal was constructed by combining spontaneous and evoked components according to the desired SNR. The structure of power spectrum of the spontaneous component was determined based on the power law, and its parameter values were selected according to the distribution of parameters from real signals. Furthermore, the power spectrum of the evoked component was generated based on the signal-to-noise ratio and the power spectrum value of the spontaneous component at the stimulation frequency and its harmonics. Evaluation of the temporal waveform, frequency component power, and the correlation distribution between real and artificial signal samples, in comparison with results of previous research methods, indicates the effectiveness of the proposed approach. This method enables the generation of artificial signals with a specified SNR and statistical characteristics similar to real SSVEP signals, in any quantity, with minimal cost and time. This research represents a significant step toward the development of SNR estimation methods in biological signals.