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A time-domain algorithm for fiber Bragg grating simulation is formulated. It provides a time-domain equivalent to the well-known spectral-domain transfer matrix algorithm for fiber Bragg grating simulation, and allows much more accurate impulse response to be simulated directly from a known fiber Bragg grating. Two different time-domain grating reconstruction algorithms are formulated, which are much more accurate and efficient than their spectral-domain equivalents due to their intrinsic infinite spectral representation and truly one-dimensional nature. Error studies are also conducted for the time-domain grating reconstruction algorithms. The high accuracy and efficiency of the new time-domain algorithms are well demonstrated with several simulation, reconstruction, and design examples.