Based on a discrete grating model,the time-domain transfer matrix and scattering matrix are deduced.According to the causality analysis,a full time-domain algorithm for fiber Bragg grating(FBG)synthesis is proposed which can also be used to directly calculate the impulse response of a known FBG in time domain.It employs simple transforms and shift operations in the iterations and takes the feedback between multiple reflectors into account,which enable it suitable for reconstructing strong gratings.The superiority of the full time-domain algorithm is illustrated by the numerical simulations of grating synthesis.