Compositionally step-graded ((Al)Ga)_xIn_1−xP (x=0.52–0.22) buffers and following In_0.3Ga_0.7As cap layers are grown by metal-organic chemical vapor deposition on (001) GaAs substrates with different miscuts toward (111)A. The tilt with respect to the substrate and phase separation in Ga_xIn_1−xP buffer layers are investigated by x-ray reciprocal space mapping and transmission electron microscopy. It is found that a large negative tilt is generated in the [110] direction due to the preferential nucleation of α dislocations with tilt component along [001¯], and that a positive tilt in the [11¯0] direction is introduced by the wavy surface undulations along [11¯0] when growing the Ga_xIn_1−xP buffer and enhanced by preferential glide of the existing β dislocations in the (1¯11) slip plane during the growth of the In_0.3Ga_0.7As cap layer. The phase separation in the Ga_xIn_1−xP buffer layer, acting as the main source of threading dislocations in the In_0.3Ga_0.7As cap layer, has been suppressed by increasing the number of steps in the buffer layer and thickness and utilizing (Al_0.3Ga_0.7)_0.22In_0.78P layer as the top buffer layer. Finally, In_0.3Ga_0.7As layers with a low threading dislocation density are obtained on the top AlGaInP layer due to the lattice hardening effect and this improvement is confirmed by the photoluminescence measurements.