The new Laplace variational iterative method is used in this research for solving the (2+1)-D and (3+1)-D Burgers equations. This technique relies on the modified variational iteration method and the Laplace transform. To apply this approach, the differential problem is first transformed into an algebraic form using the Laplace transform, and then the algebraic equations are iteratively solved using the modified variational iterative approach. By utilizing this technique, the Burgers equations can be solved both numerically and analytically. The study demonstrates the effectiveness of the new Laplace variational iterative approach through three specific examples.