The polymer particles of the invention are characterized by being obtained by polycondensation of at least one from among Compound 1 represented by general formula (1), its hydrolysates and its partial condensates, and at least one from among Compound 2 represented by general formula (2), its hydrolysates and its partial condensates, and by having a mean particle size of 3-1000 nm. M(OR1)z  (1) (R2)nM(OR3)z-n  (2) where M is Al, Si, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ge, Zr, Nb, Mo, Sn, Sb, Ta, W, Pb or Ce; z is the atomic valence of M; R1 and R3 are each an alkyl group of 1-5 carbon atoms, an acyl group of 1-6 carbon atoms or an aryl group of 1-9 carbon atoms; R2 is a monovalent organic group of 1-8 carbon atoms; n is an integer of from 1 to (z−2); and R1, R2 and R3 may be the same or different. These particles are used in polishing compositions used for chemical mechanical polishing.