This paper discusses a novel Bayesian estimation method for the residential gas demand function in Japan where the price per unit decreases as the demand exceeds certain thresholds. Such a price system is known as decreasing block rate pricing. The demand function under decreasing block rate pricing is derived by using the well-known discrete/continuous choice approach. However, because of the nonconvex budget set, the conventional approach imposes highly nonlinear constraints on the model parameters, thus making the maximization of the likelihood function under such constraints difficult to implement. To overcome this difficulty, we first apply the duality relationship in consumer theory, and approximate the conditional expenditure in order to linearize these nonlinear constraints. Then, we adopt a Bayesian approach with the Markov chain Monte Carlo simulation in order to estimate the model parameters under linear constraints. Our proposed method is illustrated by a numerical example and is adopted to analyze the demand for residential gas in Japan.