The invention provides a positive electrode active substance, a positive electrode containing the positive active substance and a battery including the positive electrode. The positive active substance contains a crystal mixture containing a first crystal and a second crystal, wherein the first crystal is selected from one or more of compounds represented by LixxM'yy (XO4) zz, LiM'XO5, LiM'XO6, and LiM'X2O7, where the ratio of xx to zz is larger than 0 and not larger than 1, and the ratio of yy to zz is larger than 0 and not larger than 1.1; and the second crystal is one or more of compounds represented by LiDcO2, LiiNi(1-d-e)CodMneO2, LiNi(1-f-g) CofAlgO2, LixNi(1-y) CoO2 and LimMn(2-n)EnOj, where D is one element selected from B, Mg, Al, Ti, Cr, Fe, Cu, Zn, Ga, Y, La and V, c is larger than 0 and not larger than 3, i is not less than 0.9 and not larger than 1.2, d is not less than 0 and not larger than 0.5, e is larger than 0 and not larger than 0.3, f is not less than 0 and not larger than 0.5, g is not less than 0 and not larger than 0.3, x is not less than 0.9 and not larger than 1.1, y is not less than 0 and not larger than 1; E is one of B, Mg, Al, Ga and a transition metal except Mn, m is not less than 0.9 and not larger than 1.1, n is not less than 0 and not larger than 1, and j is larger than 1 and less than 6. The positive active substance has an electron conductivity of 0.001 to 10 S/cm at 25 DEG C, and can remarkably improve the specific discharge capacity and the cycle performance of the battery.