Erbium-doped lithium niobate on insulator (Er∶LNOI) has attracted much attention because of its high gain. The Er∶LNOI waveguide amplifier is modeled and the corresponding energy-level rate equation is established. The gain performance of Er∶LNOI waveguide is simulated by using the model and compared with experiments. The internal net gains of the amplifier at the signal wavelength of 1531.5 nm and 1550.0 nm are studied at 980 nm and 1484 nm pump wavelengths. The waveguide gains with different signal powers and pump powers are compared by experiment and simulation. In addition, the effect of waveguide length on amplifier gain is also investigated.