In cryptographic protocols, the agent’s epistemic and doxastic states are changeable over time. To model these dynamics, a time-dependent cryptographic protocol logic is proposed. Our logic is based on the predicate modal logic and the time factor can be expressed in it by invoking a time variable as a parameter of predicates and modal operators. This makes it possible to model every agent’s actions, knowledges and beliefs at different time points. We also give the formal semantics of our logic to avoid the ambiguity of its language and make the logic sound. The semantics is based on the kripke structure and the possible world in it is built both on the local world of agent and the specific world of time. This makes every possible world can give a global view of each point of the protocol. Our logic provides a flexible method for analyzing the cryptographic protocols, especially the time-dependent cryptographic protocols, and increases the power of the logical method for analyzing protocols.