Theoretic design of Er 3+-Yb 3+ co-doped phosphate glass (LGS-L) waveguide amplifier was performed by a rate-equation formalism with overlapping integral method. Numerical results demonstrate that, for the Er 3+-Yb 3+ co-doped phosphate glass (LGS-L) fabricated by authors with an Er 3+ concentration of 1.51×10 26 ion/m3 and a Yb 3+ concentration of 19.1×10 26 ions/m3, a gain of 2.6 dB/cm can be obtained, and more than 15 dB gain at an Er 3+ concentration of 2.0×10 26 ions/m3 for amplifier length of 4 cm is possible. Furthermore, effects of the overlapping between lateral distribution of optical fields(signal and pump) and that of Er 3+(Yb 3+) co-doped on gain and optimum length and effects of the ratio of Yb 3+ to Er 3+ doped on gain at a pumping wavelength of 980 nm are discussed.