The delay characteristic of the Brillouin slow light using broadband pump with rectangular spectrum is analyzed. Analytical expressions of the time delay,the pulse-width broadening ratio and the gain of a Gaussian pulse are deduced under small-signal gain approximation. Calculated results show that the analytical solution and the numerical solution agree well and the Gaussian signal pulse can achieve zero-broadening delay,when its 10 dB bandwidth is not greater than 0.357-fold pump bandwidth. The maximum Brillouin gain bandwidth for a broadband pump with single rectangular spectrum is 20 GHz,indicating that zero-broadening delay of the Gaussian pulse with full-width at half maximum of about 100 ps can be achieved. Broadband pump light with rectangular spectrum is more favorable for reducing the pulse distortion than that with Gaussian spectrum.