The π-calculus is one of the most important mobile process calculi and has been well studied in literatures. Temporal logic is thought as a good compromise between description convenience and abstraction and can support useful computational applications, such as model-checking. In this paper, we use symbolic transition graph inherited from π-calculus to model concurrent systems. A wide class of processes, that is, the finite-control processes can be represented as finite symbolic transition graph. A new version modal logic for π-calculus, an extension of the modal ?-calculus with boolean expressions over names, and primitives for name input and output are introduced as an appropriate temporal logic for the π-calculus. Since we make a distinction between proposition and predicate, the possible interactions between recursion and first-order quantification can be solved. A concise semantics interpretation for our modal logic is given. Based on the above work, we provide a model checking algorithm for the logic. This algorithm follows the well-known Winskel?s tag set method to deal with fixpoint operator. As for the problem of name instantiating, our algorithm follows the ?on-the-fly? style, and systematically employs schematic names. The correctness of the algorithm is shown.