A Cosmological Model without Singularity and Dark Matter Shi-Hao Chen Institute of Theoretical Physics, Northeast Normal University, Changchun 130024, China. shchen@nenu.edu.cn (Dated:; Received text; Revised text; Accepted text; Published text) According to the cosmological model without singularity, there are s-matter and v-matter which are symmetric and have oppose gravitational masses. In V-breaking s-matter is similar to dark energy to cause expansion of the universe with an acceleration now, and v-matter is composed of v- F-matter and v-W-matter which are symmetric and have the same gravitational masses and forms the world . The ratio of s-matter to v-matter is changeable. Based on the cosmological model, we confirm that big bang nucleosynthesis is not spoiled by that the average energy density of W-matter (mirror matter) is equal to that of F-matter (ordinary matter). According to the present model, there are three sorts of dark matter which are v-W-baryon matter (4/27), unknown v-F-matter (9.5/27) and v-W-matter (9.5/27) . Given v-F-baryon matter (4/27) and v-W-baryon matter can cluster and respectively form the visible galaxies and dark galaxies. Unknown v-F-matter and v-W-matter cannot cluster to form any celestial body, loosely distribute in space, are equivalent to cold dark matter, and their compositions are unknown. The number in a bracket is the ratio of the density of a sort of matter to total density of v-matter. The decisive predict is that there are dark celestial bodies and dark galaxies. The energy of F-matter can transform into the energy of W-matter by such a process in which the reaction energy is high enough. 1 Abstract arXiv:1001.4221v1 [physics.gen-ph] 25 Jan 2010