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 a 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. The first elements 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 frequency components are calculated in synchronism with rotation of the engine, using the first element intensities and the second element intensities. The frequency component intensities are calculated by replacing a part of an integrated value of the first element intensities, and a part of an integrated value of the second element intensities respectively with corresponding preceding calculated values, when an rotational speed of the engine is higher than or equal to a set threshold value.