Summary: We present a new and simpler axiomatization for the three-valued modal propositional logic defined by P. Ostermann [Z. Math. Logik Grundlagen Math. 34, 343-354 (1988; Zbl 0661.03011)]. We define a canonical model and a filtration for this logic, and we prove three-valued versions of the Truth and Filtration Lemmas, well-known results in propositional modal logic. We obtain a new proof for the completeness of the smallest three-valued normal logic 3-K. Also, 3-K has the finite model property. These results can be easily extended to three-valued versions of other systems of propositional modal logic.