The local mean decomposition (LMD) is a relatively new approach of adaptive signal analysis. The core of LMD is to decompose the original signal into several product functions (PF), and each of which is a product of an envelope signal and a purely frequency modulated signal. Both the local mean and envelope estimate of the signal needs to be extracted in the LMD algorithm, while the conventional extraction approach brings the local error and in a slow rate of decomposition. To solve these problems, a new approach of extracting the local mean and envelope estimate using the cubic B-spline interpolation (CBI) is proposed. The upper envelope and the lower envelope are obtained by the CBI firstly, and then the local mean and envelope estimate are extracted from these two envelopes. The comparative experiments with simulated signals and mechanical vibration signals verified the superiority of this new approach.