Based on the well-known ( empirical) stylized facts such as infinite activity Lévy jump，stochastic volatility and leverage effect，this paper extends non-Gaussian OU stochastic volatility model，which is pro- posed by Barndorff-Nielsen and Shephard，driven by infinite activity Lévy jump processes. Then the European option pricing model is studied by FFT technology and the principle of structure preserving martingale measure the specific expressions of BNS models driven by different Lévy processes ( Gaussian process，Gamma process and CGMY process) under the risk neutral measures are obtained. Efficient MLE-SMC algorithm，joint sample estimation algorithm and gradient-SMC algorithm are given to estimate the parameters and latent variables of non-Gaussian OU stochastic volatility models using stock and option prices. Finally，in contrast to most exist- ing studies，our model assessment—an empirical research based on the 4. 7 million price data of S&P500 op- tions—is not restricted to the fitting performance，but even takes into account factors like model stability，the exposure to risks arising from the model calibration and the ability to explain observed prices of options. The empirical results show that the pricing effect of in-the-money options is superior to that of the out-of-the-money options. In most cases，the pricing effects of our BNS option pricing models based on joint sample estimation algorithm and gradient-SMC algorithm are better than that of MLE-SMC algorithm.