This paper is entirely devoted to analyze and solve the H-2 optimal state feedback sampled-data control design problem of Markov Jump Linear Systems. Several theoretical aspects are addressed, in particular, mean square stability and performance optimization. The numerical procedure follows by embedding the system under consideration into a more general class of dynamical systems named Hybrid Markov Jump Linear System. Hence, the state feedback sampled-data control gains are calculated from the solution of a new and specific two-point boundary value problem. A global uniformly convergent algorithm based exclusively on linear matrix inequality is proposed. The theory is illustrated by means of practical examples. (C) 2015 Elsevier Ltd. All rights reserved.