Living things produce hard tissues such as bones, teeth and shells through precipitation of inorganic substances such as calcium carbonate (CaCO3), hydroxyapatite (Ca10(PO4)6(OH)2) and silica (SiO2) on organic matrices at ambient conditions. This phenomenon is called biomineralization. As a novel technique to develop inorganic-organic hybrid materials, biomimetic process which mimics the mechanism of the biomineralization have been attracting much attention. This paper reviews some trials to obtain inorganic-organic hybrids based on calcium carbonate and hydroxyapatite. Crystal structure and morphology of the calcium carbonate can be easily controlled according to the kind of organic polymers and metal ions added into calcium carbonate supersaturated solutions. In addition, various hydroxyapatite-polymer hybrids can be designed by using simulated body fluid (SBF) or more concentrated solutions that is supersaturated with respect to the hydroxyapatite. This type of biomimetic process is expected as a novel material design with low energy consumption and low load on environment.