We theoretically investigate dynamics of two dark solitons in a polariton condensate under nonresonant pumping,based on driven dissipative Gross-Pitaevskii equations coupled to the rate equation.The equation of motion of the relative center position of two-dark soliton is obtained analytically by using the Lagrangian approach.In particular,the analytical expression of the effective potential between two dark solitons is given.The resulting equation of motion captures how the open-dissipative character of a polariton Bose-Einstein condensate affects properties of dynamics of two-dark soliton,i.e.,two-dark soliton relax by blending with the background at a finite time.We further simulate the relative motion of two dark solitons numerically with the emphasis on how two-soliton motion is manipulated by the initial velocity,in excellent agreement with the analytical results.The prediction of this work is sufficient for the experimental observations within current facilities.