The transfer mechanism from the amplitude noise of the coupling light to the phase noise of the probe light in a Rydberg electromagnetic induced transparency effect derived from a ladder-type system including 6S1/2↔6P3/2↔62D5/2 of Cs atoms is demonstrated by using Mach-Zehnder interferometer and balanced homodyne detection technology. In our experiments, the transmission signal of 852 nm probe light is measured by scanning the coupling light frequency nearby the transition from 6P3/2 to 62D5/2 Rydberg state, while the frequency of the probe light is locked at the resonance transition of the 6S1/2↔6P3/2. The relative phase stability of two arms of Mach-Zehnder interferometer, which is constructed with the first order diffraction light of probe light through an acoustic-optic modulator, is accomplished by the controlled piezoelectric ceramic with the PID feedback loop. The interferences between the probe light and the reference light of Mach-Zehnder interferometer under the different relative phases are observed. The interference spectrum of probe light is in good agreement with the theoretical simulation result of the ladder-type three-level system. Therefore, we study the transfer characteristics from the frequency noise of coupling light to the phase noise of probe light when coupling light frequency resonance happens at the transition 6P3/2↔62D5/2. We find the significant suppression of the phase noise of probe light at the higher frequency noise. Moreover, we observe the characteristics of the phase noise of the probe light varying with the power of the coupling light under the different detuning degrees of coupling light. In the red detuning side, the transferred phase noise of probe light decreases with the increase of coupling light power, which is different significantly from the scenario under the blue detuning condition. The ions produced in the ionization process of Rydberg atoms will form the local electric field that would cause the energy level of Rydberg states to shift. The investigation of the noise transfer between the coupling light and probe light in the Rydberg electromagnetically induced transparency effect is important for understanding the coherence mechanism of ladder-type system and the some potential applications, such as in Rydberg-atom-based electric field metrology.