Pedestrian counting has attracted much interest of the academic and industry communities for its widespread application in many real-world scenarios. While many recent studies have focused on computer vision-based solutions for the problem, the deployment of cameras brings up concerns about privacy invasion. This paper proposes a novel indoor pedestrian counting approach, based on footstep-induced structural vibration signals with piezoelectric sensors. The approach is privacy-protecting because no audio or video data is acquired. Our approach analyzes the space-differential features from the vibration signals caused by pedestrian footsteps and outputs the number of pedestrians. The proposed approach supports multiple pedestrians walking together with signal mixture. Moreover, it makes no requirement about the number of groups of walking people in the detection area. The experimental results show that the averaged F1-score of our approach is over 0.98, which is better than the vibration signal-based state-of-the-art methods.