We fabricated tantalum pentoxide (Ta₂O₅) channel waveguides and used them to experimentally demonstrate higher-order mode supercontinuum (SC) generation. The Ta₂O₅ waveguide has a high nonlinear refractive index which was in an order magnitude of 10^-14 cm²/W and was designed to be anomalously dispersive at the pumping wavelength. To the best of our knowledge, this is the first time a higher-order mode femtosecond pump based broadband SC has been measured from a nonlinear waveguide using the phase-matching method. This enabled us to demonstrate a SC spectrum spanning from 842 to 1462 nm (at - 30 dB), which corresponds to 0.83 octaves, when using the TM₁₀ waveguide mode. When using the TE₁₀ mode, the SC bandwidth is slightly reduced for the same excitation peak power. In addition, we theoretically estimated and discussed the possibility of using the broadband higher-order modes emitted from the Ta₂O₅ waveguide for trapping nanoparticles. Hence, we believe that demonstrated Ta₂O₅ waveguide are a promising broadband light source for optical applications such as frequency metrology, Raman spectroscopy, molecular spectroscopy and optical coherence tomography.