The purpose of this paper is to estimate the cost inefficiency of Japanese municipal hospitals using the stochastic cost frontier approach. It is assumed that hospital cost inefficiency has a truncated normal distribution in order to avoid the restrictive feature of the half-normal distribution. A model of hospital cost inefficiency in which the inefficiency is a function of some explanatory variables was defined. The stochastic cost frontier and the inefficiency model were estimated simultaneously. The results indicate that the half-normal distribution is not appropriate for the inefficiency distribution of municipal hospitals in Japan. It is also found (i) that the level of cost inefficiency is related to the government subsidy and the geographical location of the hospital; and (ii) that, when compared to the truncated normal cost inefficiency model, the half-normal model underestimates the marginal costs while it overestimates the cost inefficiency.