Turbomachinery with double counter-rotating impellers offer more degrees of freedom in the choice of design and control parameters compared to conventional machines. For these innovative machines, the literature review shows that more published works are available concerning axial type turbomachines than centrifugal ones. This work deals with a preliminary design and performance analysis applied to two counter-rotating impellers of a centrifugal compressor. We present here the design practice developed based on 0D/1D models, also coupled with optimization and stream-curvature through-flow methods to satisfy the selected design-criteria. An analyze of aerodynamic performances results are made and compared to those available experimental and numerical data of a baseline configuration, composed of one centrifugal-impeller and a volute. The compressor studied here includes a first conventional impeller with an axial inlet and a mixed or centrifugal outlet. The second impeller is designed parametrically and can be considered as a rotating-diffuser with a radial or mixed inlet and outlet. Ultimately, the numerical simulation results of a selection of candidate solutions are discussed.