We consider a two-dimensional asymmetric nozzle jet flow impinging on a flat wall. The flow issuing from nozzle orifice makes free boundaries between fluid and surrounding air. Although the governing equation is harmonic, the free boundaries make the problem highly non-linear. We propose an efficient algorithm to find the free boundaries of the asymmetric jet emanating from arbitrary nozzle. Using the boundary integral equations, our method can find the gradient toward the solution from the assumed free boundaries. Particularly, by considering the far-field behavior of solution, our algorithm can deal with the entire computational domain instead of truncated one. In the numerical results, the force exerted on the wall by the pressure and numerical calculations of diverse examples are shown.