A fiber Bragg grating(FBG)which could transform a single pico-second optical pulse to a doubled optical pulse pair was designed by using Fourier transformation method.The designed FBG consists of a grating with index modulation distribution as a pair of sinc function.The characteristics of the reflected pulses from the designed FBGs with different reflectivity were examined by numerical calculation.The intensity difference between two output pulses was increased with increasing of the FBG reflectivity,while the output pulses would have the same shape of the input pulse.When the FBG is weak,i.e.with lower reflectivity,the output doubled pulses will have the same amplitude,same pulse shape and same pulse width with the input pulse.When the FBG becomes strong,the amplitudes fo the two output pulses will be different.They can have the same amplitude if the FBG is made of a pair of sinc function with different amplitudes.