In a uniform fiber Bragg grating, if the input signal is a Gaussian pulse the dispersion is zero near center wavelength and becomes appreciable only near the band edges and side lobes of the reflection spectrum. However for chirped Gaussian pulses, group velocity dispersion and the reflected light must become asymmetric. Here the chirped Gaussian pulses can be treated as a symmetric but nonuniform input signal. The present paper describes that for the case of symmetric Gaussian pulse, the group velocity dispersion and pulse distortion remain symmetric however strong the grating may be. On the other hand both tend to be more asymmetric for the case of strong grating while the input signal is symmetric with nonuniform shape