The success of ISOMAP depends greatly on being able to choose a suitable neighborhood size, however, it is still an open problem how to do this effectively. Based on the fact that “short circuit” edges pass the area with the relatively lower local densities, this paper presents a new variant of ISOMAP, i.e. P-ISOMAP (pruned-ISOMAP), which can prune effectively “short circuit” edges existed possibly in the neighborhood graph and thus is much less sensitive to the neighborhood size and more topologically stable than ISOMAP. Consequently, P-ISOMAP can be applied to data visualization more easily than ISOMAP because the open problem described above can be avoided to the utmost extent. The effectivity of P-ISOMAP is verified by the experimental results very well.