Based on the theory of the second-order intensity moment and the method of Fourier transformation, some parameters for a broadband Gaussian beam in free space are studied analytically and numerically. It is shown that the beam width and the divergence angle for a broadband Gaussian beam in free space are both larger than those for a monochromatic Gaussian beam. The broader the bandwidth of a light beam, the larger the beam width and the divergence angle of the light beam. The beam propagation factor for a broadband Gaussian beam in free space is larger than that for a monochromatic Gaussian beam and increases slowly with bandwidth. The kurtosis parameter for a broadband Gaussian beam in free space increases with propagation distance and bandwidth. The kurtosis parameter for a broadband Gaussian beam with much broader bandwidth increases more remarkably with propagation distance.