I will give a proof of an integrality of p-adic multiple zeta values. I would also like to explain how it can be applied to give an upper bound of the dimension of finite multiple zeta values. Two errata on the proof of Theorem 1. 1. The claim ``we have canonical lifts of Frobenius on Z_T and Z_U" is not correct. It should read ``we have canonical lifts of Frobenius on the p-adic completions of Z_T and Z_U". 2. The weight filtration on the module H does not satisfy W_0 H = H. It should read W_{-1}H = 0.