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In this article, the Laplace decomposition method is implementedto solve nonlinear partial differential equations. Third-order KdVand mKdV equations with initial conditions have been considered to checkthe validity of the proposed method. Results obtained by this methodare compared with the exact solutions in literature numerically as well asgraphically and are found to be in good agreement with each other. Theproposed method finds the solutions without any discretization, perturbation,linearization, or restrictive assumptions. Obtained results show thatthe LDM is highly accurate and easy to apply for NLPDEs in variousfields.AMS (MOS) Subject Classification Codes: 44A10; 35Q53; 35C08; 35C10Key Words:Laplace Decomposition Method, KdV and mKdV equations, Adomian polynomial,nonlinear partial differential equation.