The growth by solid source molecular beam epitaxy (MBE) of type-II InAsSb/lnAs multi-quantum well laser diodes on InAs has been studied. Strained InAsSb/InAs quantum wells were sandwiched between two A1AS(0.16)Sb(0.84) 2 mum-thick cladding layers, lattice-matched to InAs. The precise control of the composition of the thick A1AsSb ternary alloy was obtained using a quasi-stoichiometric growth (QSG) method, which requires a determination of the incorporation rate of each element. This rate was obtained from reflection high-energy electron diffraction (RHEED) intensity oscillations. Alloys composition was entirely controlled by Sb-2 flux, suggesting a sticking coefficient close to unity. Mesa-stripe laser diodes processed from the epitaxied structures operated at 3.5 mum in pulsed regime up to 220 K, with a threshold current density of 130 A/cm(2) at 90 K and a peak optical power efficiency of 50 mW/A/facet.