In the non-relativistic limits, long pulses and ultra-short pulses laser propagation characteristics in the fully-ionized plasma are discussed. The electron density distribution can be derived from the balance of the pondermotive force with the thermal force in long pulses and with the electrostatic force in ultra-short regime. Using the source-dependent expansion (SDE) method, the laser field propagation characteristics in plasma can be described through the numerical solution of the enveloped equation. In long pulses, the self-guiding, which means the laser spot size oscillates in the spread direction, will appear if the ratio of the laser power and the plasma temperature exceeds the threshold. The guiding cannel is steady in some initial laser spot size and the optimal condition to produce the narrowest steady channel is found. In ultra-short pulses, the effective Rayleigh length of laser increases but self-guiding does not occur according to the numerical solution and theoretic analysis.