This paper discusses a curve-fitting technique based on the first-order linear ordinary differential equation model for predicting the solution of dynamic systems. First, a least squares optimization problem is defined to minimize the differences between the system and the model. It is assumed that the system’s actual solution exists. Second, the model parameters are updated iteratively by applying the gradient method, in turn, to minimize the mean square errors and to determine the model’s solution optimally. When convergence is achieved, the optimal parameters employed in the linear model give a best-fit solution to the system solution with a minimum mean square error value. Third, a chemical reaction model consisting of three nonlinear ordinary differential equations is studied for illustration. The simulation results show the accuracy of the curve-fitting solution to dynamic systems with a small mean square error value. Hence, the technique’s efficiency is demonstrated, and the best fitting of the nonlinear dynamic system using the linear model is satisfied.