In this paper, the impact of growth parameters on the strain relaxation of highly lattice mismatched (11.8%) GaSb grown on GaP substrate by molecular beam epitaxy has been investigated. The surface morphology, misfit dislocation and strain relaxation of the GaSb islands are shown to be highly related to the initial surface treatment, growth rate and temperature. More specifically, Sb-rich surface treatment is shown to promote the formation of Lomer misfit dislocations. Analysis of the misfit dislocation and strain relaxation as functions of the growth temperature and rate led to an optimal growth window for a high quality GaSb epitaxial layer on (001) GaP. With this demonstrated optimized growth, a high mobility (25,500 cm(2) V (-1) s(-1) at room temperature) AlSb/InAs heterostructure on a semi-insulating (001) GaP substrate has been achieved.