Abstract: In this study, a variable step size approach is adopted in implementing Implicit Block Multi-step Method for solving non-stiff ordinary differential equations. This idea has many computational advantages when compared with other methods. They include designing a suitable step size/changing the step size, stopping criteria (prescribed tolerance level) and error control/minimization. This approach utilizes the estimates of the principal local truncation error on a pair of explicit and implicit of Adams type formulas which are implemented in P(CE)m mode. Gauss Seidel approach is employed for the implementation of the proposed method. Numerical experiments are given to show the efficiency of the method.