CdTe is an important optoelectronic material in the IR range application. CdTe was grown on InSb(001) by molecular beam expitaxy (MBE). Low temperature (2K) photoluminescence (PL) spectra were measured at c4fferent excitation power level while laser beam was focused on the same spot of the sample. From our experiment, we can obtain that the spectral features in the 1.4-1.5 eV range consist of three sets of DAP recombination emissions with different values of Huang-Rhys constants. Their peak positions are shifted with the excitation power at different rates. As expected, the Huang-Rhys factor is larger for the broadband feature than other two processes, i.e. this DAP transition involves c4fferent mechanisms from the two others.