By use of photoconductive switches triggered by the ultrafast femtosecond pulses in the terahertz (THz) time-domain spectroscopy (TDS) system,the optical phonon oscillation characteristics of isomorphs KTiOPO4 (KTP) and its crystallographic isomorphs RbTiOPO4 (RTP) crystals are studied in the 0.5-2.0 THz range. Although the two crystals have quite similar lattice structure,their terahertz spectrums reveal different characteristics:the absorption of the RTP crystal is stronger than that of the KTP crystal,and the peaks of related optical phonon oscillation of the RTP crystal are more than that of the KTP crystal while the polarization of terahertz field parallels to the z-axis of the crystals. With pseudo-harmonic dielectric model,the complex dielectric constant curves of the two crystals are calculated,and the parameters related to the optical phonon resonances are obtained. The results demonstrate that all these phonon oscillation peaks in terahertz range are corresponding to the optical external modes which are caused by the vibrations of the K (or Rb) ions with the screw of PO4 tetrahedral and TiO6 octahedral. But since the Rb ions have more atomic weight,their chemical band strength with surrounding atoms or groups is correspondingly stronger and complex,which leads to the diversity of optical phonon oscillation modes.