The heterogeneous network, contains a macro cell and a grid of low power nodes with the same frequencies, can improve the system capacity and spectrum efficiency. Configuring low-power nodes that share the same spectrum with macro cell to form heterogeneous networks makes it more likely to improve the system capacity and spectrum efficiency, but inevitably, strong co-channel interference is the main barrier to further improvement for heterogeneous networks. This paper proposes an algorithm which combines the triangular decomposition and signal to leakage and noise ratio (SLNR) (TD-SLNR) to suppress strong co-channel interference in multi-cell multiple input and multiple output (MIMO) heterogeneous networks. Firstly, the proposed algorithm can reduce the number of inter-cell interferences in half. As a result of triangular decomposition, an equivalent interference channel model is extracted to eliminate the rest of interferences using SLNR and interference suppression matrix. Theoretical analysis shows that the proposed algorithm provides a potential solution to suppress the co-channel interference with low complexity and reduce the computation complexity without adding extra interference suppression matrices and computation complexity at receivers. Furthermore, the simulation results show that TD-SLNR algorithm can improve system capacity and energy efficiency comparing with the traditional SLNR algorithm.