The two-dimensional microchannel heat sinks equipped with porous media is designed by robust topology optimization (RTO) for removing the waste heat in space constrained applications. In RTO, minimizing both the mean and the standard deviation of average temperature is regarded as the optimization objective, and the mean of the flow dissipation is constrained not higher than the threshold of the pump. And the polynomial chaos expansion coupled with continuous adjoint method is adopted to solve the sensitivity of RTO. The average performance improvement (API) as well as robustness improvement (RI) are used to compare the deterministic topology optimization (DTO) and RTO. For three flow dissipation constraint thresholds, results indicate that when the flow dissipation constraint is relaxed, the channel topology becomes denser and more complex, and the branches of topology increase in both DTO and RTO configurations. In addition, compared to the DTO configuration, the average performance of RTO configuration can improve 15.53, 13.34 and 12.09%, and the robustness of RTO can improve 26.53, 22.19 and 19.77% when the flow dissipation thresholds are set as 4.0, 7.0 and 12.5 times the straight channel configuration. When flow dissipation is constrained to 7.0 times the straight channel configuration and inlet velocity varies 0.1–0.4 m/s, the API of RTO configuration is 13.81–20.16%, and the RI of RTO configuration is consistently over 20%