This paper is devoted to the study of phonon and melting property of two-demensional PeLrose lattice with five-fold rotational symmetric axis. We introduce a similarity transformation which transforms the dynamical matrix into a block-diagonal matrix, which helps to determine analytically the degeneracies of the modes of the phonon spectra and reduce the numerical calculation. It is found that two thirds of the modes are doubly degenerate and theremains are nondegenerate. By using the atomic mean-square displacement criterion, we study the melting property of the two-demensional Penrose lattice. We find that boundary atoms always have lower melting temperature than that of bulk, and when the interaction among atoms is larger, the system will have a higher melting temperature.