Focal-plane arrays (FPAs) are often interfered by heavy fixed-pattern noise, which severely degrades the detection rate and increases the false alarms in airborne point target detection systems. Thus, high-precision nonuniformity correction is an essential preprocessing step. In this paper, a new nonuniformity correction method is proposed based on a staircase scene. This correction method can compensate for the nonlinear response of the detector and calibrate the entire optical system with computational efficiency and implementation simplicity. Then, a proof-of-concept point target detection system is established with a long-wave Sofradir FPA. Finally, the local standard deviation of the corrected image and the signal-to-clutter ratio of the Airy disk of a Boeing B738 are measured to evaluate the performance of the proposed nonuniformity correction method. Our experimental results demonstrate that the proposed correction method achieves high-quality corrections.