We present a numerical study on the evolution of the intense femtosecond pulse propagation in argon by solving the extended nonlinear Schr¨odinger equation which includes the beam diffraction, group velocity dispersion, self focusing, absorption and defocusing due to the electron density, and multiphoton ionization processes. The temporal and spatial profiles and the dynamic picture of the ultrashort pulse propagation in argon under different incident conditions such as initial peak intensity, pressure, beam radius, pulse width, and the focal length are discussed. Because the competition between the self focusing and defocusing effects accompanying with other effects as we mentioned above, we can see the splitting into two or even three peaks of the pulse in the time domain.