Reducing the losses of the tip clearance flow is one of the keys in an unshrouded centrifugal compressor design and development because tip clearances are large in relation to the span of the blades and also centrifugal compressors produce a sufficiently large pressure rise in single stage. This problem is more acute for a low flow high-pressure ratio impeller design. The large tip clearance would cause flow separations, and as a result it would drop both the efficiency and surge margin. Thus a design of a high efficiency and wide operation range low flow coefficient centrifugal compressor is a great challenge. This paper describes a recent development of high efficiency and wide surge margin low flow coefficient centrifugal compressor. A viscous turbomachinery optimal design method developed by the authors for axial flow machine was further extended and used in the centrifugal compressor design. The compressor has three main parts: impeller, a low solidity diffuser and volute. The tip clearance is under a special consideration in this design to allow impeller insensitiveness to the clearance. A patented three-dimensional low solidity diffuser design method is used and applied to this design. The compressor test results demonstrated to be successful to extend the low solidity diffusers to high-pressure ratio compressor. The compressor stage performance showed the total to static efficiency of the compressor being about 85% and stability range over 35%. The test results are in good agreement with the design.