This paper studies highly dispersive bright and dark optical solitons from a numerical perspective by variational iteration method. This is a very efficient algorithm that has gained popularity to numerically address model equations from a range of physical phenomena including photonics sciences. The current paper studies highly dispersive optical soliton solutions that are considered with quadratic-cubic nonlinear form of refractive index, modeled by the nonlinear Schrodinger's equation. The novelty of this approach is that it recovers bright and dark soliton solutions to the model numerically, and the error of approximation has also been presented. The algorithm displays the solutions with an impressive error measure.