In this study, we report the growth of core-shell InGaP nanowires with compositional varied cores/shells using metal-organic chemical vapor deposition. These core-shell InGaP nanowires exhibit Ga-enriched cores attributed to the strong affinity between Au and In, and In-enriched shells due to In-rich vapor ambient. Detailed electron microscopy investigations indicate that the In and Ga concentrations in the nanowire cores and shells varied along the growth direction of InGaP nanowires. It is found that the strain relaxation through Ga diffusion outward and In diffusion inward leads to the decrease of compositional difference between the nanowire core and shell from top to bottom. This study offers a possibility to grow structural complex ternary nanowires that can be used for future applications.