Without any additional conditions on sub-additive potentials, this paper defines sub-additive measure-theoretic pressure, and shows that the sub-additive measure-theoretic pressure for ergodic measures can be described in terms of measure-theoretic entropy and an constant associated with the ergodic measure. Based on the definition of topological pressure on non-compact set, we give another equivalent definition of sub-additive measure-theoretic pressure, and we can obtain an inverse variational principle. This paper also studies the sup-additive measure-theoretic pressure which has similar formalism as the sub-additive measure-theoretic pressure. Moreover, we prove that the zero of the non-additive measure-theoretic pressure gives the lower and upper bound estimate of dimensions of an ergodic measure.