A mass spectrometry apparatus configured to allow a user to designate an upper limit value UL together with a lower limit value, as a peak sorting condition. A data processing section is operable to determine whether respective peak intensities of a plurality of peaks appearing on a mass spectrum fall within an intensity range Ath defined by upper and lower limit values UL, LL, and exclude any peak out of the intensity range Ath. The remaining ions are selected as precursor ions, for example, in descending or ascending order of peak intensity so as to perform an MS2 analysis. The upper limit UL is adequately set to allow the MS2 analysis for a sample component with a low concentration, by priority, while avoiding a sample component exhibiting a high intensity and having no need for the MS2 analysis.