Magnetic flux leakage (MFL) inspection is one of the most important and sensitive nondestructive testing approaches. For online MFL inspection of a long-range railway track or oil pipeline, a fast and effective defect profile estimating method based on a multi-power affine projection algorithm (MAPA) is proposed, where the depth of a sampling point is related with not only the MFL signals before it, but also the ones after it, and all of the sampling points related to one point appear as serials or multi-power. Defect profile estimation has two steps: regulating a weight vector in an MAPA filter and estimating a defect profile with the MAPA filter. Both simulation and experimental data are used to test the performance of the proposed method. The results demonstrate that the proposed method exhibits high speed while maintaining the estimated profiles clearly close to the desired ones in a noisy environment, thereby meeting the demand of accurate online inspection.