By using photoluminescences (PL), the molecular beam epitaxy (MBE) grown Hg1-xCdxTe (x=0.32) epilayers are studied. The PL measurement shows a strong near band edge emission peak with an FWHM of 5 meV and a small broadening energy, E0(4.2 K)=1.3 meV, which indicates the high quanlity was obtained. Comparing the results of as-grow and annealing sample shows that annealing sample has a better crystal quality than the as-grow sample.