Accurate Doppler scale estimation and compensation in the challenging underwater acoustic (UWA) communication channels are the essential requirement for the performance of the orthogonal frequency division multiplexing (OFDM) systems. In UWA OFDM systems, increasing the correlation accuracy between the received cyclic prefix (CP) and OFDM symbol for Doppler scale estimation depends on the sampling rate of the signal. Increased sampling rate results in an increased accuracy at the cost of an increased computational complexity. Therefore, in this paper, we adopted a less computational complex auto-correlation approach, where we first derived the closed form expression for auto-correlation based Doppler scale estimation in CP-OFDM signal, and then proposed three different fine Doppler scale estimation methods. From the simulations, it is observed that in single path channel, methods 2 and 3 perform better in terms of RMSE and BER, while method 1 shows better performance in multipath channels.