In this paper, we propose a dynamic secure routing game framework to effectively combat jamming attacks in distributed cognitive radio networks. We first propose a stochastic multi-stage zero-sum game framework based on the directional exploration of ad hoc on-demand distance vector (AODV) algorithms. The zero-sum game captures the conflicting goals between malicious attackers and honest nodes and considers packet error probability and delay as performance metrics. The game-theoretic routing protocol guarantees a performance level given by the value of the game. Distributed Boltzmann-Gibbs learning is used for an on-line routing algorithm, in which the users do not have the knowledge of the attackers and the utility function. Instead, the users learn the payoffs based on their past observations. We use simulations to illustrate the proposed routing mechanism and compare the algorithm with fictitious-play learning. Unlike typical distributed routing algorithms such as AODV routing, the proposed secure routing algorithm supports a novel recovery of routing path failure against unknown attackers.