In this paper I consider the effects of a minimum price in a search model with price posting. It is well known that a maximum price only affects the upper support of the price offer distribution in Burdett and Judd (1983). I show that with a minimum price, there will be a mass point, and if it is sufficiently high, the price distribution will become degenerate. I also show that under some matching technology, the decentralized market equilibrium can have too little entry, and a minimum price could achieve the social optimum.