Computational speed plays a critical role in the application of the Finite Element Method (FEM), especially when the number of elements is relatively large. The calculation speed of FEM depends on two factors including the speed of calculating the overall system of linear algebraic equations and the convergence speed. This report presents the neighbor node technique to speed up calculating the overall system of linear algebra equations, thereby reducing computational time in FEM. This technique increases the speed of traditional solving methods such as Gauss, Gauss Jordan, Gauss–Seidel, and Successive Overrelaxation (SOR). When the number of elements is large enough, the time of computing the system of linear algebraic equations using the neighbor node technique reduces significantly compared to without applying the technique. For example, the Gauss method with the neighbor node technique solves the system of overall linear algebraic equations approximately 2 times faster than without applying the technique.