This paper presents a local geometric projection (LGP)-based noise reduction technique for vibration signal analysis in rolling bearings. LGP is a nonlinear filtering technique that reconstructs one dimensional time series in a high-dimensional phase space using time-delayed coordinates based on the Takens embedding theorem. From the neighborhood of each point in the phase space, where a neighbor is defined as a local subspace of the whole phase space, the best subspace to which the point will be orthogonally projected is identified. Since the signal subspace is formed by the most significant eigen-directions of the neighborhood, while the less significant ones define the noise subspace, the noise can be reduced by converting the points onto the subspace spanned by those significant eigen-directions back to a new, one-dimensional time series. Improvement on signal-to-noise ratio enabled by LGP is first evaluated using a chaotic system and an analytically formulated synthetic signal. Then, analysis of bearing vibration signals is carried out as a case study. The LGP-based technique is shown to be effective in reducing noise and enhancing extraction of weak, defect-related features, as manifested by both the multi-fractal and envelope spectra of the signal.