This paper addresses the extremal problem of the null subcarriers based Doppler scale estimation in underwater acoustic(UWA) orthogonal frequency division multiplexing(OFDM) communication. The cost function constructed of the total energy of null subcarriers through discrete Fourier transform(DFT) is proposed.The frequencies of null subcarriers are identified from non-uniform Doppler shift at each tentative scaling factor. Then it is proved that the cost function can be fitted as a quadratic polynomial near the global minimum. An accurate Doppler scale estimation is achieved by the location of the global scarifying precision and increasing the computation minimum through polynomial interpolation,without complexity. A shallow water experiment is conducted to demonstrate the performance of the proposed method. Excellent performance results are obtained in ultrawideband UWA channels with a relative bandwidth of 67%, when the transmitter and the receiver are moving at a relative speed of 5 kn, which validates the proposed method.