In order to nd the approximate solution of the KdV equation, we use the nite element method of Taylor-Petrov-Galerkin, in which discretization in the time variable is carried out using Taylor series expansion and for discretization in space are considered as test functions cubic B-splines and Legendre polynomials as weight functions. These functions are adequate in that they satisfy continuity, integrability and orthogonality required to apply the method.