The treatment of boundary condition at multiple outlets is one of the key issues in the numerical simulation of aero-engine combustors， as the mass flow ratios need to be within the engineering design limits， and the numerical stability needs to be ensured with recirculating flow at the outlets. In the present paper， an incompressible flow outlet boundary condition algorithm is developed to treat the boundary condition at multiple outlets with recirculating flow and specified flow ratios. The results of a series of numerical experiments show that stable and convergent solutions can be obtained using the proposed method. Cases of tetrahedral/hexahedral meshes and the mass flow ratio ranging from 0 to 1.0 are simulated， and the obtained maximum deviation is <0.001%. When the mass flow ratios at the multiple outlets are fixed， the resulted velocity profiles are not obviously affected by the location of outlet boundaries when the flows at the boundaries are not fully-developed or even recirculating. The proposed method is applied to the simulation of TECFLAM swirl burner. The predicted velocity components agree well with the experimental data even when the computational domain is truncated to one third of the original size. Compared to the conventional treatment of outlet boundary conditions， the method proposed enables to specify the mass flow ratios at multiple outlets and to adjust computational domain sizes according to the engineering design limits， which contributes to significant reduction of the overall computational cost.