Based on a coordinate transformation, the boundary potential of a quantum rods was changed from the ellipsoidal form into an spherical one. The properties of the vibrational frequency, first internal excited state energy, excitation energy and frequency of transition spectral line between first internal excited state and ground state of weak-coupling polaron in a quantum rod in a parabolic potential are studied by using linear combination operator and unitary transformation methods. Relations of the vibrational frequency, first internal excited state energy, excitation energy and frequency of transition spectral line of polaron with transverse and longitudinal effective confinement length, aspect ratio of the ellipsoid and electron-phonon coupling strength were derived. Numerical calculation results show that the vibrational frequency, the first internal excited state energy, excitation energy and frequency of transition spectral line increase rapidly with decreasing transverse and longitudinal effective confinement length. The vibrational frequency and first internal excited state energy are decreasing functions of the aspect ratio of ellipsoid and electron-phonon coupling strength, respectively. The excitation energy and frequency of transition spectral line are increasing functions of the aspect ratio when e′>1, whereas it is decreasing function of one when e′<1. When e′=1, the excitation energy and frequency of transition spectral line have minimum values.