Disclosed is a wireless signal receiving apparatus, and more particularly, disclosed is a parallel automatic frequency offset estimation apparatus and method for tracking a frequency offset in an early stage by calculating, in parallel, frequency offsets of a received signal. The parallel automatic frequency offset estimation apparatus includes a receiving unit to receive a data frame; and a frequency offset estimation unit to calculate, in parallel, frequency and phase deviations at different bit intervals within a particular section of the received data frame, to add together the frequency and phase deviations to obtain a first sum of the frequency and phase deviations, and to add the first sum to a frequency phase deviation calculated for each bit after the particular section in the received data frame to obtain a second sum of the frequency and phase deviations. Accordingly, transmission frequency tracking can be performed at higher speed, compared to the conventional systems in which frequency offset acquisition is carried out in stages. Also, accurate tracking of a transmission frequency is possible in an initial frame.