The invention relates to the field of flow measurement, in particular to a coriolis mass flowmeter plus-minus phase-step alternative excitation vibration-starting method and a system thereof. The system comprises a magnetoelectric velocity transducer, a voltage follower, a low-pass filtering amplifier, a biasing circuit, a limiter circuit, an audio-frequency CODEC (coder decoder), a DSP (display signal processor), a DDS (direct digital synthesizer), an amplifier, a MDAC (multiplication digital-to-analog converter), a power amplifier and a vibration exciter. The vibration amplitude of a flow tube can be enlarged continuously, reliably and rapidly by tracking phases of self-excitation output signals of detecting sensors and carrying out plus-minus phase-step alternative excitation, and the vibration-starting time of the flow tube can be shortened greatly with the combination of non-linear amplitude control algorithm and frequency estimation algorithm.