A method is proposed for analyzing the NMR relaxation data. The procedure includes using the nonnegative leastsquares (NNLS) to determine roughly the relaxation time values. Then those values are used as the initial parameters of the nonlinear fitting computation. As a result, accurate relaxation time data can be conveniently obtained without any preknowledge of the sample. This method is verified and demonstrated by computer simulations and NMR experimental results.