This paper discasses the electronic coherence affected by the voltage and the position of quantum-interference transistor''s gate on one arm of metallic ring of mesoscopic system. The theoretical results indicate that, generally changing the length L₆ of the gate(the length L₂ of the lower arm) can make transmissivity have the periodic variation whose period is π(2π), and simultaneously it is found that the position of quantum-interference transistor''s gate on the arm doesn''t influence the periodicity of the transmissivity, but only changes the size of the transmissivity ,and the period of transmissivity as function of kL₂ will be π when kL₆ is equal to nπ; quantum-interference transistor will not influence the coherence of electronic transmissivity when kL₆ is equal to (2n+1)[]2π;the transmissivity will be permanently equal to 1, and irrelevant with the length of the gate and the position of quantum-interference transistor''s gate on the arm when kL₂and kL are both equal to nπ.