This paper proposes a primal decomposition algorithm for efficient computation of multistage scenario model predictive control, where the future evolution of uncertainty is represented by a scenario tree. This often results in large-scale optimization problems. Since the different scenarios are only coupled via the so-called non-anticipativity constraints, which ensures that the first control input is the same for all the scenarios, the different scenarios can be decomposed into smaller subproblems, and solved iteratively using a master problem to co-ordinate the subproblems. We review the most common scenario decomposition methods, and argue in favour of primal decomposition algorithms, since it ensures feasibility of the non-anticipativity constraints throughout the iterations, which is crucial for closed-loop implementation. We also propose a novel backtracking algorithm to determine a suitable step length in the master problem that ensures feasibility of the nonlinear constraints. The performance of the proposed approach, and the backtracking algorithm is demonstrated using a CSTR case study. (C) 2019 The Authors. Published by Elsevier Ltd.