To investigate the impact of geometric nonlinearity on human-induced vibrations of flexible suspension bridges, a nonlinear finite element model of a flexible pedestrian suspension bridge is established based on an engineering background and validated using measured results. Subsequently, nonlinear transient vibration analysis of the suspension bridge, considering geometric nonlinearity, is conducted. This analysis reveals the structural displacement response time histories and time-frequency characteristics under different main cable sag-to-span ratios and excitation amplitudes, as well as the response-excitation amplitude curves. The results indicate that single-frequency excitation at low-order vertical modes can induce high-order frequency vibrations at 1∶2 and 1∶3 ratios. When the ratio of vertical to horizontal natural frequencies is close to 2∶1, a certain level of vertical excitation on the main girder can cause lateral sway of the structure. Increasing the main cable sag-to-span ratio can effectively suppress vertical and lateral coupling vibrations. As the vertical excitation level increases, the sway amplitude exhibits a sudden jump and significant increase at a critical excitation level. Under pedestrian-induced excitation, the flexible suspension bridge exhibits significant geometric nonlinear vibration characteristics.