In this work, we present a numerical method based on parametric adaptive cubic spline functions for solving generalized long wave equation. The truncation error is investigated. Stability analysis of the method based on the von Neumann technique is studied and the method is shown to be unconditionally stable. Three invariants of motion are calculated to determine the conservation properties of the problem. The efficiency of the methods is demonstrated by test problems. The numerical simulations can validate and demonstrate the advantages of the method.