Direct ion-beam lithography was used to realize the staircase-like second order distributed feedback grating formed in the top cladding layers of ring quantum-cascade laser. As a result, the depth of grating slits was varied from 0.6  to 2.6 μm along the ring cavity. The whispering gallery modes lasing with near 1 kA/cm2 threshold current density at 77 K temperature was obtained with lasing wavelength close to 7.64 μm. Rise of the temperature up to 292 K yields  the multi-mode lasing near to 7.94 μm with moderate threshold current density ~4 kA/cm2. Time-resolved spectral characterization results are also discussed.