We study the nonreciprocal modification of Flat-top optical pulses via a one-dimensional photonic band-gap structure with Weyl semimetal-based defect layers due to their wide range of applications, such as high-speed communication, nonlinear optical switching, and ultrafast pump-probe experiments. We apply the transfer matrix method to obtain the transmission spectrum of the structure. Also, the Fourier transform technique is used to investigate the effect of the propagation direction of the incoming pulse on the temporal profile of the outgoing pulse. Then we examine the impact of the carrier frequency and duration of the incoming pulse on the length, energy, and magnetic field distribution of the outgoing pulse. It is shown that the temporal profile of an incoming flat-top pulse may modify to a nearly flat-top, oscillatory single-peak, or multi-peak profile depending on the carrier frequency, duration, and propagation direction of the incoming pulse.