The author deals with a multistage stochastic linear programming problem. In detail, he considers a nonanticipative case and a finite underlying probability space. Consequently, the considered multistage stochastic programming problem can be represented in a tree like form and moreover, with each note of the decision tree a certain linear or quadratic subproblem can be associated. The aim of the paper is to present a parallel decomposition method solution of the above introduced optimization problem. It is proven that the suggested method after a finite time either discovers inconsistency in the problem or finds an optimal solution. An illustrative example is given at the end of the paper.