A flight-of-time mass spectrometer is offered which can provide a variable range of collisional energies that can be made wider than heretofore. Also, a method of controlling this spectrometer is offered. The spectrometer has an ion source, a first mass analyzer, an ion gate, a potential lift, a collisional cell, a second mass analyzer, a detector, and a potential control portion for controlling the potential on the potential lift. When the precursor ions selected by the ion gate enter the potential lift, the potential control portion sets the potential on the conductive box at V1. When the potential on the potential lift is varied, the potential control portion varies the potential on the potential lift from V1 to V2 while precursor ions are traveling through the potential lift.