The Hamiltonian of a quantum rod with an ellipsoidal boundary is given after a coordinate transformation, which changes the ellipsoidal boundary into a spherical one. The first excited state energy, excitation energy and the transition frequency between the first excited state and ground state of the weak-coupled impurity polaron in it were studied. The effects of the transverse and longitudinal effective confinement lengths, the Coulomb bound potential and the ellipsoid aspect ratio are taken into consideration by using linear combination operator and unitary transformation methods. It is found that these quantities are increasing functions of the Coulomb bound potential, whereas are decreasing functions of the aspect ratio and the effective confinement lengths. These can be attributed to the interesting quantum size confining effect.