Artificial neural networks (ANNs) can help camera-based remote photoplethysmography (rPPG) in measuring cardiac activity and physiological signals from facial videos, such as pulse wave, heart rate and respiration rate with better accuracy. However, most existing ANN-based methods require substantial computing resources, which poses challenges for effective deployment on mobile devices. Spiking neural networks (SNNs), on the other hand, hold immense potential for energy-efficient deep learning owing to their binary and event-driven architecture. To the best of our knowledge, we are the first to introduce SNNs into the realm of rPPG, proposing a hybrid neural network (HNN) model, the Spiking-PhysFormer, aimed at reducing power consumption. Specifically, the proposed Spiking-PhyFormer consists of an ANN-based patch embedding block, SNN-based transformer blocks, and an ANN-based predictor head. First, to simplify the transformer block while preserving its capacity to aggregate local and global spatio-temporal features, we design a parallel spike transformer block to replace sequential sub-blocks. Additionally, we propose a simplified spiking self-attention mechanism that omits the value parameter without compromising the model's performance. Experiments conducted on four datasets-PURE, UBFC-rPPG, UBFC-Phys, and MMPD demonstrate that the proposed model achieves a 12.4\% reduction in power consumption compared to PhysFormer. Additionally, the power consumption of the transformer block is reduced by a factor of 12.2, while maintaining decent performance as PhysFormer and other ANN-based models.