Coherent frequency conversions using multiband topological edge states in photonic structures made of nonlinear optical materials have been extensively investigated. In practice, however, coherent sources localized at the subwavelength scale are of great importance. Herein, efficient second-harmonic generation (SHG) using dual-band second-order topological corner states is reported. By properly adjusting the structural parameters, dual-band corner states can be obtained in the first and second bandgaps, when the eigenfrequency of the corner state in the higher bandgap is twice that of the corner one in the lower gap. In a square lattice made of tellurium as an example, high SHG efficiency in the order of 10⁻¹% can be obtained for a peak pump intensity of around 20 GW cm⁻². The results presented provide the realizability of subwavelength-scale coherent sources, which are robust against the structural disorder or defects.