The performances of radio on fiber (RoF) systems with a dual-electrode Mach-Zehnder modulator and an erbium-doped fiber amplifier (EDFA) are optimized by numerical equations including the third order intermodulation (IM3) as well as amplified spontaneous emission (ASE) noise. We investigate a signal-to-noise-and-distortion ratio (SNDR) considering fiber dispersion with respect to an input signal power and an EDFA gain in both noise-dominant and third order intermodulation (IM3)-dominant cases. We also verify that the numerical analysis results are well matched with those of a commercial simulator, VPItransmissionMaker. In the analysis results, the optimum input signal power for the maximum SNDR of a RoF system with EDFA was reduced over 8 dB compared with that without EDFA. The dramatic reduction of IM3 power at a receiver was resulted from this decrement of input signal power. Thus, the maximum SNDR of the system with EDFA was obtained over 17 dB at 40 km fiber compared with that of the system without EDFA. In addition, the results showed that the SNDR was efficiently improved by EDFA in the noise-dominant case, while the SNDR improvement was negligible by EDFA in the IM3 dominant case.