Maclaurin expansion near zero domain is applied to analysis the difference form of the normalized nonlinear Schrdinger equation in frequency domain, and a rapid numerical difference recurrence formula is deduced in time domain, which considers the nonlinear Kerr effect as well as the effect of chromatic dispersion in optical medium simultaneously. Through some examples, a comparison is made between the results using the algorithm of this paper and the known analytical results, including the results of SSFM method. The calculated results show that this method has not only fairly fast calculation speed, but also very high calculation precision, and is more suitable to the actual situation of light pulse propagation affected by the dispersion and nonlinearity at the same time through optical medium. All the above results show that it is a well founded, fast and effective numerical calculation method to study light pulse propagation in optical medium.