The aim of this paper is to show some equidistribution statements of Galois orbits of CM-points for quaternion Shimura varieties. These equidistribution statements will imply the Zariski densities of CM-points as predicted by Andre-Oort conjecture (see Section 2). Ourmain result (Corollary 3.7) says that the Galois orbits of CM-points with themaximalMumford-Tate groups are equidistributed provided that some subconvexity bounds onRankin-Selberg L-series and on torsions of the class groups. A proof of the subconvexity bound for L-series has been announced by Michel and Venkatesh. Combining with some work of Cogdell, Michel, Piatetski-Shapiro, Sarnak, and Venkatesh, we obtain the following unconditional results about the equidistribution of CM-points in the following cases. (1) Full CM-orbits on quaternion Shimura varieties (Theorem 3.1). This is a generalization of the work of Duke [11] for modular curves, Michel [20], and Harcos and Michel [16] for Shimura curves over Q. (2) Galois orbits of CM-points with a fixed maximal Hodge-Tate group (Corollary 3.8). Under our setting, this strengthens a result of Edixhoven and Yafaev [15] about the finiteness of CM-points on a curve with fixed Q-Hodge structure.