Starting from the vector potential and the scalar potential in the Lorentz gauge, the nonparaxial beam propagation is studied in free space. Applying Fourier transform and angular spectrum, the equation has been derived for transverse electric fields of an arbitrary polarized electromagnetic wave with the new approximation and multiscale perturbative method, the analytical solution for Gaussian beam propagation beyond the paraxial approximation is accessed. For weakly nonparaxial beams that are characterized by small values of the perturbative parameter, our corrective solictions yield an accurate description of the field in the near-field regin. We firstly give the eighth correction solution, our correction, solutions yield an accurate description of the field in the near-field region. In addition, the lowest-order correction to the paraxial approximation can be found to be the Gaussian.