This study presents an approach to estimate the characteristics of multiple narrow-opening cracks from magnetic flux leakage (MFL) signals. The number, locations, orientations and lengths of the cracks are the objective of the inversion process. The proposed procedure provides a reliable estimation of crack parameters in two separate consecutive steps. In the first step, the Canny edge detection algorithm is used to estimate the number, locations, orientations and lengths of the cracks. Then, an inversion procedure based on space mapping is used in order to estimate the crack depths efficiently. The accuracy of the proposed algorithm is examined via simulations based on the finite element method as well as real experimental MFL data.