There have been many researches and rich results on the system risk in bank network systems that use complex network theory. Researches to date focus on the relationship between the contagion of the risk and the structure of the network after risk bursting, based on the assumptions that the accumulation of the system risk in network systems has approached the critical point of bursting and that the network is static (both the node and connection of the bank network are static).However, the problem why the system risk accumulates gradually and finally bursts in the network has not been addressed yet. The study on the system risk accumulation can only be conducted in dynamically evolving bank network systems; and the risk can be observed clearly only if the system risk is evaluated quantitatively. Therefore, a dynamically evolving complex bank network system, which has nodes of dynamic behavior and exhibits macroeconomic trends, is modelled first in the present paper. A lending-borrowing algorithm and a multi-term clearing algorithm for the dynamic bank network system are designed, and the method for calculating the system risk is proposed also. Finally, the system risk is calculated and analyzed by simulation. The curve of the system risk evolving with time is shown and the process of the accumulation of the system risk can be observed clearly. Researches in the present paper are to lay a foundation for the quantitative study of the system risk accumulation in dynamically evolving bank network systems.