This paper analyzes the multivariate stochastic volatilities with a common factor which is affecting both the volatilities of crude oil and agricultural commodity prices in both biofuel and non-biofuel use. We develop a stochastic volatility model which has a latent common volatility with two asymptotic regimes and a smooth transition between them. In contrast with conventional volatility models, stochastic volatilities in this study are generated by a logistic transformation of the latent factors, which consists of two components: the common volatility factor and the idiosyncratic component. In this study, we analyze the stochastic volatility model with a common factor for oil, corn and wheat from August 8, 2005 to October 10, 2014 using a Markov-Chain-Monte-Carlo (MCMC) method and estimate the stochastic volatilities and also extract the common factor. Our results suggest that the volatility of oil and grain markets are very persistent since the common factor generating the stochastic volatilities of oil and commodity markets is highly persistent. In addition, the volatilities of oil prices are more affected by a common factor while the volatilities of corn are more determined by the idiosyncratic component.