In this paper, an improved scene-based non-uniformity correction (SBNUC) algorithm called space projection estimator and temporal iteration (SPETI) is proposed. This method estimates the global translation by the projection estimator and iterates between several adjacent frames. The detailed method includes three main steps. First, we develop a new projection estimator for the registration with a criterion. Then, correlation of adjacent frames, together with iteration strategy between them, is used in order to get fast and reliable fixed-pattern noise (FPN) reduction with low few ghosting artifacts. Finally, this algorithm is immigrated into an FPGA-based hardware system. We test the performance of our algorithm by the evaluation indexes, and demonstrate the actual effect of correcting the non-uniformity under a monotonous motion on the system. In order to compare with the gated adaptive least mean square (GALMS) method and the total variation (TV) method, a clean infrared image sequences with synthetic non-uniformity is studied. Normal distributed gain and offset non-uniformity are applied to the image sequences to study the relationship of iteration times and level of non-uniformity.