Abstract: The response functions of the ex-core detector represent the contribution of fission neutron in the core to the response of the detector. The response function can be calculated efficiently by the adjoint S_N transport calculation. However, the result of the S_N method is distorted by the ray effect because the ex-core detector is far away from the core and is very small in size relative to the core. In order to overcome this problem, the adjoint first-collision source method was studied. Moreover, the parallel calculation method and dynamic memory management method were also implemented to ensure the massive adjoint first-collision source calculation efficiency. Calculations based on the Korean Kori-1 reactor indicate that the S_N method with adjoint first-collision source ray effect elimination technique has the comparable accuracy with multi-group Monte-Carlo method, and can achieve much higher efficiency.