The generalized LR parsing algorithm for context-free grammars is extended for the case of Boolean grammars, which are a generalization of the context-free grammars with logical connectives added to the formalism of rules. In addition to the standard LR operations, Shift and Reduce, the new algorithm uses a third operation called Invalidate, which reverses a previously made reduction. This operation makes the mathematical justification of the algorithm significantly different from its prototype. On the other hand, the changes in the implementation are not very substantial, and the algorithm still works in time O(n⁴).