Demand for organic and conventional vegetables is investigated using data from A.C. Nielsen’s 2006 Homescan panel. We use a Bayesian Markov chain Monte Carlo technique, along with data augmentation, to estimate a large linear approximate Almost Ideal Demand System with censored dependent variables. Demands are price elastic, and expenditure elasticities are very high for organic vegetables, whilst demands for conventional vegetables are primarily inelastic. We find a mix of gross substitution and complementarity among the vegetable products, but net substitution is the dominant pattern. Socio-demographic characteristics also play important roles in demands. These findings can inform deliberations about marketing campaigns, nutrition education and policy interventions.