High-precision spectra of Rydberg atoms are of significance in studying the interaction between Rydberg atoms, the energy level structure of Rydberg atom, and the precision measurement of the electromagnetic field. To enhance the measurement sensitivity, it is necessary to achieve the high contrast, high signal-to-noise ratio, and narrow linewidth of the spectra of the Rydberg atoms. In this work, the cavity-enhanced spectra of Rydberg atoms are studied theoretically and experimentally. Comparing with the free-space spectra of Rydberg atoms, the contrast and the signal-to-noise ratio are enhanced by 11.5 times, with the linewidth unchanged. Under the condition of two-photon resonance, both the electro-magnetically induced transparency and the double-resonance optical-pumping process can suppress the absorption of the probe laser, thereby improving the impedance matching of the cavity. As the intracavity probe laser intensity turns stronger, the contrast and signal-to-noise ratio can be improved further, and the improvement depends on the transmission of the probe laser through the atom vapor. It is expected that the contrast and signal-to-noise ratio can be improved by a factor of 23 through optimizing the temperature of the cesium atom vapor. This work provides an important reference for improving the contrast of the spectra of Rydberg atoms and the sensitivity of Rydberg-based precision measurements.