Model checking is an effective technique for automatically verifying the behavior of hardware and software systems. To formally verify a concurrent system that contains non-deterministic and inconsistent information, based on the possibility theory and multivalued logic, we propose a generalized possibilistic multivalued model checking algorithm for computation tree logic with multi-valued decision process (MvDP), and apply it to non-deterministic system verification. Firstly, an MvDP is constructed to specify the behaviour of the system as a formal system model. Then a multi-valued computation tree logic (MvCTL) is introduced to describe system properties and the model checking algorithm of generalized possibilistic MvCTL with MvDP is presented. The algorithm converts the model checking problem into polynomialtime fuzzy matrix calculations. Finally, we give a specific application example to deal with model checking problems of nondeterministic multi-valued systems.