In this paper, a fast orthogonal matching pursuit (OMP) algorithm based on optimized iterative process is proposed for sparse time-varying underwa-ter acoustic (UWA) channel estimation. The channel estimation consists of calculating amplitude, delay and Doppler scaling factor of each path using the received multi-path signal. This algorithm, called as OIP-FOMP, can reduce the computationally complexity of the tra-ditional OMP algorithm and maintain accuracy in the presence of severe inter-carrier interference that exists in the time-varying UWA channels. In this algorithm, repeated inner product operations used in the OMP algorithm are removed by calculating the candidate path signature Hermitian inner product matrix in ad-vance. Efficient QR decomposition is used to estimate the path amplitude, and the problem of reconstruction failure caused by inaccurate delay selection is avoided by optimizing the Hermitian inner product matrix. The-oretical analysis and simulation results show that the computational complexity of the OIP-FOMP algorithm is reduced by about 1/4 compared with the OMP algo-rithm, without any loss of accuracy.