The present paper primarily tests and verifies the effect of NMF in blind source separation of three-dimensional simulative fluorescence spectra, and then four different computational algorithms (multiplicative iterative; alternating least square; second order method; projected gradient algorithm) were used in three practical phenolic compounds(cresol, phenol, thymol) overlapping fluorescence spectra to find out which nonnegatively constrained algorithms is the most efficient for fluorescence spectra unmixing. The experiments demonstrate that four ways have the normalized residuals below 006%, and alternating least square(ALS) is the best at both convergence behavior and robustness.