In this work, we use the inverse design method to design three-channel and four-channel dual-mode waveguide crossings with the design regions of 4.32 µm-wide regular hexagon and 6.68 µm-wide regular octagon, respectively. Based on the highly-symmetric structures, the fundamental transverse electric (TE0) and TE1 modes propagate through the waveguide crossings efficiently. Moreover, the devices are practically fabricated and experimentally characterized. The measured insertion losses and crosstalks of the three-channel and dual-mode waveguide crossing for both the TE0 and TE1 modes are less than 1.8 dB and lower than -18.4 dB from 1540 nm to 1560 nm, respectively. The measured insertion losses of the four-channel and dual-mode waveguide crossing for the TE0 and TE1 modes are less than 1.8 dB and 2.5 dB from 1540 nm to 1560 nm, respectively, and the measured crosstalks are lower than -17.0 dB. In principle, our proposed scheme can be extended to waveguide crossing with more channels and modes.