We study spectral properties of charmonia in the vector and pseudoscalar channels at nonzero momenta on quenched lattices focusing on the dispersion relation and the weight of the peak. The spectral functions of charmonia are studied by the maximum entropy method with the lattice Euclidean correlation functions on the anisotropic quenched lattices. The errors of the dispersion relations and the residues of the peak are analysed in the maximum entropy method. We find a significant increase of the masses of charmonia in medium. We also find that the functional form of the dispersion relations is not changed from that in the vacuum within the error even at $T=1.6T_c$.