The set covering(SC) problem is the problem of covering all the rows of an $m{ imes}n$ matrix of ones and zeros by a subset of columns with a minimal cost. It has many practical applications of modeling of real world problems. The SC problem has been proven to be NP-complete and many algorithms have been presented to solve the SC problem. In this paper we present hybrid simulated annealing(HSA) algorithm based on the Simulated Annealing(SA) for the SC problem. The HSA is an algorithm which combines SA with a crossover operation in a genetic algorithm and a local search method. Our experimental results show that the HSA obtains better results than SA does.