This paper presents a new signal processing method based on Complex Bandpass Filtering (CBF) applied to the Coriolis Mass Flowmeter (CMF). CBF can be utilized to suppress the negative frequency component of each sensor signal to produce the corresponding analytic form with reduced tracking delay. Further processing of the analytic form yields the amplitude, frequency, phase and phase difference of the sensor signals. In comparison with previously published methods, CBF offers short delay, high noise suppression, high accuracy and low computational cost. A reduced delay is useful in CMF signal processing especially for maintaining flowtube oscillation in two/multi-phase flow conditions. The central frequency and the frequency range of the CBF method are selectable so that they can be customized for different flowtube designs.