Double-layer micro/mini channel heat sinks have great potential in the thermal management for integrated chips. In this work, two bi-objective optimization design of mini-channels is implemented using the variable density topology optimization method to get two topological single-layer mini-channel heat sinks (SL-MHSs). Among them, the SL-MHS obtained with the minimization of average temperature and power dissipation as the optimization objectives is named S1, while the SL-MHS obtained with the minimization of temperature variance and power dissipation as the optimization objectives is named S2. Then, S1 and S2 are used as the upper/lower layer of the double layer mini channel heat sink (DL-MHS), respectively. Therefore, four different topological DL-MHSs including D11, D12, D21 and D22 are achieved by assembling S1 and S2. Subsequently, the flow and thermal characteristics of the four topological DL-MHSs and conventional straight DL-MHS (C1) are studied numerically. The results show that when Re = 315, compared with C1, the maximum temperature of the substrate of the topological DL-MHSs (D11, D12, D21 and D22) can be respectively reduced by 17.0,16.6, 14.0 and 13.6 K, while the Nusselt number can be improved by 27.3%, 26.6%, 27.1% and 26.4%, respectively. Additionally, the total thermal resistance is also reduced at least 20%. However, although topological DL-MHSs produce higher pressure drop penalty, the PEC values of topological DL-MHSs are always greater than 1, which indicates that the new topological DL-MHSs is meaningful. Finally, the flow and thermal characteristics of the best one D11 are investigated experimentally. The simulated results agree well with the experimental results.