Quantum cascade (QC) lasers based on strain-compensated InxGa(1-x)As/InyAl(1-y)As grown on InP substrate using molecular beam epitaxy is reported. The epitaxial quality is demonstrated by the abundant narrow satellite peaks of double-crystal X-ray diffraction and cross-section transmission electron microscopy of the QC laser wafer. Laser action in quasi-continuous wave operation is achieved at lambda approximate to 3.6-3.7 mum at room temperature (34 degreesC) for 20 mum x 1.6 mm devices, with peak output powers of similar to 10.6mW and threshold current density of 2.7kA/cm(2) at this temperature.