A family of solutions called iso-diffraction ultra-short pulsed Hermite Gaussian beams （UPHGB） are obtained based on the paraxial propagation equation. The propagation of UPHGB is investigated in detail. The examples shows that: the nonuniformlly distributed group velocity causes the time delay at the beam periphery, which in turn induces the deviation of the transverse distribution from the Hermite Gaussian function. In propagation, the number of pulse polarity inverions varies with the order of the UPHGB. And this phenomenon originates in the difference between the group velocity and the phase velocity in UPHGB.