A Si₃N₄ slot waveguide has the ability to confine light tightly in the slot, shows weak absorption of 980 nm pump light, and has lower transmission loss compared to a Si slot. Hence, the optical waveguide amplifier based on Er³⁺ and Yb³⁺codoped was proposed to be integrated with a Si₃N₄ slot to increase the gain. The core-shell NaYF₄/NaLuF₄: 20%Yb³⁺, 2%Er³⁺ nanocrystals-polymeric methyl methacrylate covalent linking nanocomposites were synthesized and filled into the slot as gain medium. The concentrations of Er³⁺ and Yb³⁺ were increased compared with traditional physical doping methods. High-efficiency emission at 1.53 μm was achieved under 980 nm laser excitation. The slot waveguide was accurately designed using the semivector finite difference method in combination with the maximum confinement factors and the minimum effective mode area. The optimum width of the slot was 200 nm, and the optimum height and width of the silicon strip waveguide were 400 nm and 400 nm, respectively. The six-level spectroscopic model was presented, and the gain characteristics of the slot waveguide amplifier were numerically simulated. A net gain of 8.2 dB was achieved, which provided new ideas and directions for waveguide amplifiers.