This paper presents a specific and innovative implementation of cultural algorithm, which attempts to solve the assignment problem using a simplified computational procedure, which in our view is considered to be efficient than genetic algorithm. It consists of a population component almost identical to that of the genetic algorithm and, in addition, a knowledge component called the belief space. As the assignment problem is a “N men – N jobs” combinatorial optimization problem with a constraint that a single job can be assigned to only one person in such a way that the overall cost is minimized; Here the constraint that the man or job which involves the least cost and largest cost as well are availed as the knowledge component and is used to build the belief space.