The evolution equations for the parameters of the optical Gaussian-shaped pulse in optical fibers are derived by means of variational method from the MNLS equation. Then three important restricted relations between amplitude and width, frequency and chirp, width and chirp are obtaimed. Analytical solution about the width of pulse evolving on the propagation distance is also obtained. The influence of the third-order dispersion on the propagation properties of optical gaussian-shaped pulses in optical fibers is discussed.