We demonstrate widely tunable single-mode V-coupled-cavity lasers emitting at wavelengths near 3 µm based on a type-II interband cascade (IC) structure. The mode selection is achieved using a half-wave V-coupler designed for the IC structure in the mid-infrared range. The laser waveguides and cavity structure are deeply etched in a single etching step, without any grating. By changing the injection current at a fixed heat-sink temperature, a tuning range over 35 nm can be achieved with a side-mode suppression-ratio up to 28 dB. The tuning range can be extended to 60 nm when combined with the adjustments of the heat-sink temperature.