There has been considerable efforts to increase the efficiency of explicit Runge–Kutta (ERK) methods over the years. However, this always lead to increase in the number of terms of the Taylors’ series incremental function. In this work, a 3-stage geometric explicit Runge–Kutta method for solving autonomous initial value problems in ordinary differential equations is derived and implemented. The computational results show that the method is stable, efficient and accurate. We also compared this method with some other conventional methods.