To facilitate the development of on-chip integrated mid-infrared multi-channel gas sensing systems, we propose a high-power dual-mode (7.01 and 7.5 μm) distributed feedback quantum cascade laser based on stacked 3D monolithic integration. Longitudinal mode control is achieved by preparing longitudinal nested bi-periodic compound one-dimensional Bragg gratings along the direction of the cavity length in the confinement layer. Additionally, transverse coherent coupling ridges perpendicular to the cavity length direction are fabricated in the upper waveguide layer to promote the fundamental transverse mode output when all ridges are in phase. Stable dual-wavelength simultaneous emission with a side-mode suppression ratio of more than 20 dB was achieved by holographic exposure and wet etching. The entire spectral tuning range covers nearly 100 nm through joint tuning of the injection current and heat-sink temperature. High peak power and beam quality are guaranteed by the parallel coherent integration of seven-element ridge arrays. The device operates in a fundamental supermode with a single-lobed far-field pattern, and its peak output power reaches 3.36 W in pulsed mode at 20°C. This dual-mode laser chip has the potential for in-situ on-chip simultaneous detection of ${\mathrm{CH}}_4$ and ${\mathrm{C}}_2{\mathrm{H}}_6$ gases in leak monitoring.