SVOM is a Sino-French space mission targeting high-energy transient astrophysical objects such as gamma-ray bursts. The soft X-ray part of the spectrum is covered by the Micro-channel X-ray Telescope (MXT) which is a narrow field telescope designed to precisely localize X-ray sources. This paper presents the method implemented on-board to characterize and localize X-ray sources with the MXT. A specific localization method was developed to accommodate the optical system of the MXT, which is based on “Lobster-Eye” grazing incidence micro-pore optics. For the first time, the algorithm takes advantage of cross-correlation techniques to achieve a localization accuracy down to 2 arcmin with less than 200 photons, which guarantees a rapid follow-up for most of the gamma-ray bursts that SVOM will observe. In this paper, we also study the limitations of the algorithm and characterize its performance.