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The main goal of this paper is to study, analyse and prove the global convergence property of a nonmonotone semismooth Newton method. Based on this property, we aim to exploit an adaptive nonmonotone line search method and apply it for the approximate solution of elliptic optimal control problems with control constraints. To this end, we first convert the optimal control problem to a bound constrained optimization problem by using a finite-difference discretization scheme and a Newton–Cotes rule. Then we implement the adaptive nonmonotone semismooth Newton method to the resulting bound constrained optimization problem. We give some numerical examples to demonstrate the validity, efficiency and applicability of the presented method. [ABSTRACT FROM AUTHOR]