We introduce an iteration-free approach, based on a centroid algorithm with a locally adaptive threshold, for nanometer-level peak position localization of the axial response signal in confocal microscopy. This approach has localization accuracies that are near theoretical limits, especially when there is a small number of sampling points within the discrete signal. The algorithm is also orders of magnitude faster compared to fitting schemes based on maximum likelihood estimation. Simulations and experiments demonstrate the localization performance of the approach.