Time synchronization plays an important role in the scheduling and position technologies of sensor nodes in underwater acoustic networks (UANs). The time synchronization (TS) algorithms face challenges such as high requirements of energy efficiency, the estimation accuracy of the time-varying clock skew and the suppression of the impulsive noise. To achieve accurate time synchronization for UANs, an energy-efficient TS method based on nonlinear clock skew tracking (NCST) is proposed. First, based on the sea trial temperature data and the crystal oscillators’ temperature–frequency characteristics, a nonlinear model is established to characterize the dynamic of clock skews. Second, a single-way communication scheme based on a receiver-only (RO) paradigm is used in the NCST-TS to save limited energy. Meanwhile, impulsive noises are considered during the communication process and the Gaussian mixture model (GMM) is employed to fit receiving timestamp errors caused by non-Gaussian noise. To combat the nonlinear and non-Gaussian problem, the particle filter (PF)-based algorithm is used to track the time-varying clock state and an accurate posterior probability density function under the GMM error model is also given in PF. The simulation results show that under the GMM error model, the accumulative Root Mean Square Errors (RMSE) of NCST-TS can be reduced from 10⁻⁴ s to 10⁻⁵ s compared with existing protocols. It also outperforms the other TS algorithms in the aspect of energy efficiency.