Fourier series model has been widely used to represent human jumping load. This model, however, ignores the randomness in human jumping process, which may lead to uncertainties in the prediction of structural response. In this study, the human jumping load is viewed as a narrowband stationary stochastic process, and then the power spectral density （PSD） model is developed based on 334 experimental jumping load records from 73 test subjects. The PSD model was firstly derived from the measured records. A non-dimensional PSD model can be expressed by the summation of two Gaussian functions normalized from the jumping frequency and the rank order, which reflect the concentration extent and the distribution extent of jumping energy, respectively. Model parameters can be determined by equating the total energy of the proposed PSD with that of the measured PSD. In combination with the stochastic vibration theory, the computational method and steps for predicting the peak acceleration at an arbitrary location of floor were proposed. The predictions for an experimental floor model subjected to individual jumping were compared with measured peak responses. The comparison between the theoretical predictions and the experimental results indicates that the proposed PSD function is applicable for predicting the floor’s response to individual jumping. Finally, the computational framework of evaluating crowd-induced structure vibration was also discussed.