Provided is a frequency offset estimation apparatus that appropriately estimates and compensates for a frequency offset of a received signal when estimating the frequency offset which is the difference between a carrier frequency of the received signal and the frequency of an output signal of a local oscillator. The frequency offset estimation apparatus converts the received signal sampled in advance with a predetermined sampling frequency into a frequency spectrum having N frequency components, limits a frequency band of negative frequency components from 1 to N /2 of the frequency spectrum and a frequency band of positive frequency components from N /2+1 to N of the frequency spectrum, calculates the sum of the squares of the positive frequency components of the frequency spectrum that have been subjected to frequency band limitation and the sum of the squares of the negative frequency components of the frequency spectrum that have been subjected to frequency band limitation to calculate power of the positive frequency components and power of the negative frequency components, and cyclically shifts all frequency components of the frequency spectrum in a frequency domain until the absolute value of a power difference between the power of the positive frequency components and the power of the negative frequency components is less than or equal to a predetermined threshold value, and estimates the frequency offset based on a shift amount until the absolute value is less than or equal to the threshold value.