From the ultrashort pulsed Gaussian beams, based on the properties of Laguerre polynomial, a family of solutions are found in theory, which represents a new family of ultrashort pulsed beams called ultrashort pulsed elegant Laguerre-Gaussian beams. These pulsed beams with arbitrary available frequency all have a nearly elegant Laguerre-Gaussian profile, an arbitrary temporal shape, and an equal 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 Laguerre-Gaussian beams and their propagation properties in free space have been studied detailedly, such as intensity on the axis, transversal distribution of intensity, diffractive property, pulse polarity reversal, pulse time delay etc. The time and spatial singularity of the pulsed beams is also discussed when the slowly varying envelope approximation is introduced.