A frequency spectrum analyzing apparatus for performing a frequency spectrum analysis with respect to a detected value of an operating parameter of an internal combustion engine in synchronism with rotation of the engine, is provided. The operating parameter is sampled at predetermined time intervals, and the sampled value is converted to a digital value. Intensities of first and second elements are calculated with respect to a predetermined number of the sampled values, wherein the first and second elements respectively correspond to a plurality of frequency components contained in the detected value, and a phase of the second element differs from a phase of the first element by 90 degrees. Frequency component intensities corresponding to the plurality of frequencies are calculated in synchronism with rotation of the engine, using the first element intensities and the second element intensities. Offset components contained in the first element intensities and the second element intensities are calculated, and the frequency component intensities are calculated after removing the offset components from the first and second element intensities.