Near-bottom magnetic measurements on board submersible Nautile were carried out on the Mid-Atlantic Ridge 21 degrees 40'N segment, and deep-sea geomagnetic vector anomalies along 19 dive tracks were obtained by applying the processing method for shipboard three-component magnetometer data. A forward modeling technique using short-wavelength components of the anomalies arising from local topography and vertical motion of the submersible was designed to estimate the absolute magnetization intensity of the seafloor. In the vicinity of the spreading axis a considerable number of magnetization estimations are reliably confirmed by the high correlation between observed and modeled anomalies, whereas less reliable estimations are obtained off-axis, probably because the sediment buries the basement topography. The natural remanent magnetization (NRM) measured on basalt samples collected during these dives is compared with the magnetization from anomalies. Though both results give a similar range of magnetization intensity, no correlation is confirmed between them, possibly because the magnetization from anomalies represents laterally averaged seafloor magnetization, whereas the NRM has variations at the scale of individual pillow or lava pile. Equivalent magnetization inverted from the sea-surface magnetic anomalies shows axial magnetization increases significantly from the segment center to the segment ends. However, the results of eight dives conducted near the spreading axis at different locations along the segment show much less variation in magnetization intensity along the axis. We ascribe the high equivalent magnetization at segment ends to preferential serpentinization of peridotite near the segment ends and the associated formation of magnetite. The results of three across-axis transects composed of 15 dives running in the spreading direction can be consistently interpreted as recording geomagnetic paleointensity variations during the Brunhes epoch. Although magnetization lows are generally correspondent to periods of low paleointensity, they show deeper drop than predicted from the paleointensity variation.