Starting from Huygens-Fresnel diffraction integral formula, propagation expression of pulsed Bessel beams with Gaussian spectrum in frequency domain is obtained. By using Fourier transform, propagation formula of the beams in temporal domain is derived. Based on the formula, propagation properties of the beams in free space are studied through numerical calculations. It is found that bandwidth of pulse has effects on time delay and pulse width. As bandwidth broadens, the time delay increases and temporal waveform changes, which results in increasing of pulse width. The time delay and pulse width also depend on propagation distance. Both of them increase when propagation distance increases.