Pseudomorphic Iny2Al1-y2As/In0.73Ga0.27As/Iny1Al1-y1As (y1 greater than or equal to 0.52) modulation-doped heterostructures with an intentional nonlattice-matched buffer layer were successfully grown by molecular beam epitaxy on (100)InP substrates. Fourier transform photoluminescence and double crystal x-ray diffraction measurements show a superior crystalline quality in the high In content channel, when In mole fraction increases from y1=0.52 to 0.55 in the Iny1Al1-y1As buffer layer. In this case, an increasing of 16.3% and 23.5% for conductivity (mu xn(s)) and mobility, related to the strain compensation in the In0.73Ga0.27As channel, was achieved, respectively, comparing to the structure containing a well-lattice matched buffer layer. With increasing the mismatch further (y1=0.58), a morphology with cross-hatched pattern was observed due to the onset of a large amount of misfit dislocations, and the electronic characterization is not able to be improved continuously. Because we can realize high quality strained P-HEMTs in a relative wide range of equivalent beam flux (EBF) ratios, the stringent control over the constant EBF is not indispensable on this In-based material system.