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In this paper, micromagnetic simulations are employed to investigate terahertz (THz) magnetic excitations in a spin torque nano-oscillator (STNO) with a perpendicularly magnetized synthetic antiferromagnetic (SAF) free layer. The magnetization precession of the free layer can be finely tuned into the sub-THz range without the necessity of external magnetic fields. The excited frequency exhibits two distinctive regions, namely region-I and region-II, depending on the applied current strength. In region-I, characterized by relatively small currents, the two ferromagnetic layers are stabilized at two separate precession orbits. The frequency in this region decreases with current strength, exhibiting similar features as the Néel vector change observed in antiferromagnets. In contrast, region-II is defined by currents where the two ferromagnetic layers synchronize into the same precession orbit. The frequency increases with current, correlating with the variation in the net magnetization of the SAF layer. An analytical model is developed through the canonical transformation of Lagrange’s equation, which can describe the frequency dependence on both the applied current and the antiferromagnetic interlayer coupling strengths. The simulations and the analytical model show good agreement, offering a more profound understanding of the magnetic excitation properties in STNOs with ultrathin SAF free layers. These insights are crucial for the design of advanced terahertz spintronic devices.