Stochastic programming deals with optimization under uncertainty. A stochastic programming problem with recourse is referred to as a two-stage stochastic problem. We consider the stochastic programming problem with simple integer recourse in which the value of the recourse variable is restricted to a multiple of a nonnegative integer. The algorithm of a dynamic slope scaling procedure to solve the problem is developed by using the property of the expected recourse function. The numerical experiments show that the proposed algorithm is quite efficient. The stochastic programming model defined in this paper is quite useful for a variety of design and operational problems.