A second-order distributed feedback interband cascade laser emitting at 3.25 µm was designed, grown, and fabricated. By coherent epitaxy of a GaSb cap layer instead of the conventional thin InAs cap on top of the laser structure, a high-quality surface grating was made of GaSb and gold. Enough coupling strength and a significant inter-modal loss difference were predicted according to the simulation within the framework of couple-wave theory. Lasers having 2-mm-long cavities and 4.5-µm-wide ridges with high-/anti-reflection coatings were fabricated. The continuous-wave threshold current and maximum single-mode output power were 60 mA and 24 mW at 20°C, respectively. The output power of 5 mW was still kept at 55°C. Continuous tuning free from mode hopping and high single-mode suppression ratios (>20 dB) were realized at all injection currents and heat-sink temperatures, covering a spectral range of over 20 cm-1.