This paper discusses a simple heuristic to minimize the total tardiness in a single machine scheduling problem. The problem of minimizing total tardiness in single machine scheduling is a combinatorial problem. Hence, heuristic development for such problems is inevitable. In this paper, an attempt has been made to develop a simple heuristic, alternatively called greedy heuristic, to minimize the total tardiness in a single machine scheduling problem with n independent jobs, each having its processing time and due date. Further, its solution accuracy is compared with the optimal solution of a set of randomly generated problems using an ANOVA experiment. From the ANOVA experiment, it is observed that the solution of the simple heuristic proposed in this paper does not differ significantly from the optimal solution at a significance level of 0.05.