Due to the intermittency and uncertainty in photovoltaic (PV) power outputs, not only deterministic point predictions (DPPs), but also associated prediction Intervals (PIs) are important information for promoting the application of PV in practice, especially when grid connection continues to grow. While there are few studies focused on quantifying the uncertainty of forecasting PV power outputs, this paper developed a novel two-stage model to quantify the PIs of PV power outputs. In the first stage, three different neural networks, namely Generalized Regression Neural Network (GRNN), Extreme Learning Machine Neural Network (ELMNN) and Elman Neural Network (ElmanNN), were integrated using the Genetic Algorithms optimized Back Propagation (GA-BP) method to develop a Weight-Varying Combination Forecast Mode (WVCFM) model. The WVCFM model was applied to generate DPPs. In the second stage, a nonparametric kernel density estimation (NKDE) method was adopted to estimate the PIs regarding the statistical distribution of the errors of the DPPs derived in the first stage. The proposed method was tested using four types of PV output and weather data measured from a 15 kW grid-connected PV system. The cover percentage of prediction intervals (PICPs) were computed under the confidence level of 95%, 90%, 85% and 80%, respectively. The results imply that the two-stage model proposed in the paper outperforms conventional forecast methods in terms of prediction of short-term PV power outputs and associated uncertainties.