Heart Rate Variability (HRV) analysis is an important tool for health monitoring. A non-invasive smart health monitoring system based on optical fiber interferometer can get HRV information from the Ballistocardiogram (BCG) signal. For some patients, the HRV can hardly be calculated due to the interferences from breath and other vibrations. In this research, we obtain a stable and high-sensitive BCG signal by a Mach-Zehnder interferometer (MZI) based sensor. In order to reduce the noise in signal, we introduce an advanced least mean squares (LMS) adaptive filter into the procedure. We use the signal processed by a bandpass filter as the 'desired signal' to deal with the raw data and obtain a preferable output for HRV calculation.