Low-repetition rate high-power pulse-pumped Er-Yb codoped fiber amplifiers (EYDFAs) are theoretically investigated. By numerically solving the rate-equations of EYDFAs with finite difference method, in the case of limited amplified spontaneous emission (ASE), the impact of the peak-power and pulse-width of pump pulse and time-delay between signal and pump pulse on the performance of the amplifier are systematically analyzed. The results show that the pulse width of pump pulse and the time delay between the signal and pump pulses have significant impact on the performance of EYDFA. They can be optimized by controlling the power of the ASE in a reasonable range. For a given gain medium, a low peak power long pump pulse is generally better than a high peak power short pulse, and there is an optimum value. These results are of great importame in high-power pulse-pumped Er-Yb codoped fiber amplifies.