Erbium-doped waveguide amplifiers enable the integration of various active functions on a silicon platform. Er3+ can provide the basis for efficient optical amplification of photonic integrated circuits, but the gain is limited by cooperative upconversion leading to doping concentration limitations and insufficient optimization of the waveguide structure. In this paper, an erbium-ytterbium co-doped Al2O3 amplifier has been innovatively implemented on a low loss Si3N4 waveguide by careful design and optimization with the finite difference method. A more accurate and comprehensive theoretical model of erbium-ytterbium co-doping is established, with consideration of upconversions, energy transfer, amplified spontaneous radiation and propagation loss to perform optimization of the high-gain erbium-ytterbium co-doped waveguide amplifier. The optimized waveguide amplifier achieves a small-signal gain of more than 36 dB at 1550 nm under Er3+ concentration of 3 × 1020 cm-3 and Yb3+ concentration of 3 × 1021 cm-3. Endowing Si3N4 photonic integrated circuits with gain can enable the miniaturization of various on-chip based active devices.