Abstract: The use of genetic algorithm(GA) as heuristic search method to solve the single machine scheduling problems with fuzzy parameters based on possibility theory is considered.The processing times and the due dates are nonnegative fuzzy numbers and all the weights are positive,crisp numbers.For simplicity,an integer permutation as a feasible sequence to represent a candidate solution is adopted.Substring exchange crossover and shift mutation are adopted to guarantee the legitimation of offspring.Rank-based evaluation function is used to assign a probability of reproduction to each chromosome.Numerical example is provided to illustrate the effectiveness of the proposed algorithm.