Abstract: A theoretical analysis is carried out to study the evolution of a laser-induced plasma channel in air. The extended nonlinear Schr-dinger equation describing the propagation of laser pulses in air is presented and analyzed, which includes the influence of diffraction, dispersion and multiphoton ionization, Raman scattering, plasma wake fields and relativistic focusing. The electron density and the beam intensity flux along the filament are estimated by solving the Schr-dinger equation using split-step Fourier method and finite difference method. The numerical calculations confirm that the position and pattern of the filaments are dependent on the wavelength, energy, pulse duration and transverse waist of the initial laser pulse．