We report on the design of spherical composite particles (SCPs) which consist of a homogeneous distribution of metal nano-particles (Ag) in a dielectric matrix. The effective dielectric function of SCPs is described by Maxwell-Garnett effective medium theory. Within the context of Mie scattering, the extinction efficiency of SCPs in air can be specified which exhibits two different kinds of resonances;localized surface plasmon resonances (LSPRs) and dielectric resonances (DRs). Both kinds of resonances can be tuned through the permittivity of the dielectric matrix, filling fraction of the metal nano-particles, and the radius of SCPs. The special features of the localized resonances of SCPs have the potential to be used in a wide variety of applications.