We present theoretical results of a left-handed metamaterial engineered by a combination of coated and solid nano-spheres. The structure is a binary composite of CdS– TiO2 core–shell and Au solid nano-spheres which simultaneously dispersed in the air matrix. The effective medium parameters derived by extended Maxwell-Garnett (EMG) effective medium theory. It is shown the possibility of fine-tuning the metamaterial in order to observe left-handed behavior. The results are supplemented with transmittance curves, calculated by layer-multiple-scattering (LMS) method. The predictions of the EMG theory are in good agreement with those of LMS method; thus the (CdS–TiO2)/Au nanocomposite is an appropriate choice as a three-dimensional left-handed metamaterial.