We propose a dynamic tradable credit scheme for control of the day-to-day evolution process of traffic flows towards a stationary state. The double interacting dynamics between traffic flow adjustment and credit charge evolution is formulated as a dynamical system. Two properties of the dynamical system are revealed, i.e., the consistence of the stationary state with the system optimum (SO) state and the convergence of the day-to-day adjustment process. Moreover, the effect of the credit charge and issue pattern on the revenues of users is analyzed and a rule to distribute credits among all users in the day-to-day process is proposed. Finally, numerical results on both a simple network and a middle-size network are presented to show the application of the dynamic tradable credit scheme and to demonstrate the properties of the dynamical system. This study is helpful for narrowing the gap between the theory of tradable credit scheme and its application to reality.