Highly strained In0.5Ga0.5P/In0.33Ga0.67As and conventional In0.5Ga0.5P/In0.22Ga0.78As pseudomorphic high electron mobility transistor (p-HEMT) structures were grown on patterned and non-patterned GaAs substrates, respectively, by using a compound-source molecular beam epitaxy. Microwave characteristics and low-frequency noise characteristics of the p-HEMTs were measured and compared. The highly strained InGaP/In0.33Ga0.67As p-HEMT grown on the patterned substrate showed more than 20% improvements in microwave performances including the transition frequency (f(T)) and the maximum oscillation frequency (f(max)) compared with those of the conventional InGaP/In0.22Ga0.78As p-HEMT grown on the non-patterned substrate. The input noise spectral density and the Hooge parameter of the highly strained InGaP/In0.33Ga0.67As p-HEMT grown on the patterned substrate were more than an order of magnitude lower than those of the conventional InGaP/In0.22Ga0.78As p-HEMT grown on the non-patterned substrate. The improvements in microwave characteristics and low-frequency noise characteristics of the highly strained InGaP/In0.33Ga0.67As p-HEMT are attributed to the improvement in transport property of the highly strained In0.33Ga0.67As channel layer achieved by a patterned substrate growth. The results indicate the potential of highly strained p-HEMTs grown on patterned substrates for use in applications requiring improved microwave and low phase noise characteristics.