There is provided a spectrum analyzer and a spectrum analysis method capable of promptly performing measurement while preventing the spectrum waveform caused by the fractional spurious components from being displayed.When the width of a designated span (analysis target frequency range) is larger than a boundary value, a reference signal frequency is set to a predetermined reference value, and a loop filter band narrower than a RBW (resolution bandwidth) is selected to thereby make the fractional spurious components be within the RBW and prevent it from being displayed as a spectrum waveform. Further, when the width of the designated span is smaller than a boundary value, the reference signal frequency is shifted from the reference value by a predetermined value so as to increase the frequency differences between the fractional spurious components and the main signal component of a VCO output signal by an amount equal to the product between the shift amount and the integer part of the frequency division ratio, and the band of the loop filter is set in accordance with the region including the RBW in a range narrower than the increased frequency difference so as to suppress the levels of the fractional spurious components.