A closed-loop production line has a constant number of pallets (work in process, WIP) flowing through its workstations and buffers. The performance of a closed-loop production line depends not only on the machines’ reliabilities and buffers’ capacities, but also on the constant number of pallets. This paper presents an analytical method to approximate the production rate of an unbalanced closed-loop production line with finite buffers. The machines have deterministic processing times and multiple failure modes. A decomposition method was used to divide the whole line into multiple two-machine-one-buffer blocks, and the failure modes influencing the blocks are related with the constant number of pallets. An exact algorithm to calculate the production rate for continuous systems was introduced to approximate the production rate of the discrete systems. Then, interruption of flow equations and resumption of flow equations were used to iterate the whole line production rate until converging. At last, cases analysis and comparison with simulation results were used to validate the method. Especially for unbalanced closed-loop production line with different workstation time, the method also has high accuracy.