We propose for the first time, to the best of our knowledge, an on-chip integrated few-mode erbium–ytterbium co-doped waveguide amplifier based on an 800 nm thick Si3N4 platform, which demonstrates high amplification gains and low differential modal gains (DMGs) simultaneously. An eccentric waveguide structure and a co-propagating pumping scheme are adopted to balance the gain of each mode. A hybrid mode/polarization/wavelength-division (de)multiplexer with low insertion loss and crosstalk is used for multiplexing and demultiplexing in two operation wavebands centered at 1550 nm and 980 nm, where the light in these two bands serves as the signal light and pump light of the amplifier, respectively. The results demonstrate that with an input signal power of 0.1 mW, TE0 mode pump power of 300 mW, and TE1 mode pump power of 500 mW, the three signal modes (TE0/TM0/TE1) all exhibit amplification gains exceeding 30 dB, while maintaining a DMG of less than 0.1 dB.