We consider the well-known 3-valued extension of the intuitionistic propositional logic [1] and examine the conditions for o system of formulas to be complete with respect to existential expressibility of formulas considered earlier by A. V. Kuznetsov [2]. It was established that there exists a relative simple algorithm to determine whether a system of formulas is complete relative to existential expressibility of formulas in the 3-valued extension of the intuitionistic propositional logic.