Interference alignment (IA) is a promising technology to effectively eliminate interference and improve the wireless communication network capacity. However, the low complexity IA solution with high degrees of freedom (DoF) for the multi-cell multi-user cellular network is still an open problem that needs to be solved. To address this problem, in this paper, the two-stage IA scheme for the multi-cell multi-user multiple-input multiple-output (MIMO) interfering broadcast channel (IFBC) model is investigated. Since a multi-cell IFBC is a complex interfering channel model, it is simplified into several simple models. The complex MIMO IFBC model can be first transformed into a simple K-user MIMO interference channel model, by designing the first stage precoding matrix to eliminate inter-cell interference (ICI). Based on the designed first stage precoding matrix, the MIMO IFBC becomes several single-cell MIMO IFBCs, and the second stage precoding matrix can be designed to eliminate inter-user interference (IUI). The high system sum-rate performance and low computational complexity of the proposed IA design scheme are verified through a series of simulations.