Pulse distortion in a turbulent ocean is investigated using the temporal moment method. The first- and second-order temporal moments are related to the pulse arrival time and pulse width, respectively. Without dispersion in the ocean, the pulse is expected to be delayed and broadened owing to sound-speed fluctuations. The effects of the vertical sound-speed profile are included. To simplify the computations, the turbulent ocean is assumed to be statistically homogeneous and isotropic, and to follow a Gaussian correlation function. In computing the temporal moments, the coefficients in a power series expansion of the two-frequency mutual coherence function have to be evaluated in terms of the relative difference between two wavenumbers. A bilinear sound-speed profile is used. The propagation range is limited under the assumption that the ray trajectory does not pass the depth of the minimum sound speed. Numerical results show that the effects of random scattering on the arrival time are negligibly small. However, random scattering will significantly broaden the pulse, especially when the range is large.