Starting from the ultrashort pulsed Gaussian beams, a family of solutions are found theory in by using the properties of Hermite function, which represents a new family of ultrashort pulsed beams called ultrashort pulsed elegant Hermite-Gaussian beams. These pulsed beams with a certain frequency have a nearly elegant Hermite-Gaussian profile, an arbitrary temporal shape, and a common diffractive distance. These solutions can be even used to describe the ultrashort pulsed beam whose pulse duration is shorter than one optical oscillation period. The ultrashort pulsed elegant Hermite-Gaussian beams and their propagation properties in free space have been studied in detailedly, such as intensity on the axis, polarity reversal, pulse time delay etc. The spatial singularity of the pulsed beams is also discussed when the slowly varying envelope approximation is introduced.