In underwater wireless optical communication (UWOC) links, multiple scattering may cause temporal spread of beam pulse characterized by the impulse response, which therefore results in inter-symbol interference (ISI) and degrades system error performance. The impulse response of UWOC links has been investigated both theoretically and experimentally by researchers but has not been derived in simple closed-form to the best of our knowledge. In this paper, we analyze the optical characteristics of seawater and present a closed-form expression of double Gamma functions to model the channel impulse response. The double Gamma functions model fits well with Monte Carlo simulation results in turbid seawater such as coastal and harbor water. The bit-error-rate (BER) and channel bandwidth are further evaluated based on this model for various link ranges. Numerical results suggest that the temporal pulse spread strongly degrades the BER performance for high data rate UWOC systems with on-off keying (OOK) modulation and limits the channel bandwidth in turbid underwater environments. The zero-forcing (ZF) equalization designed based on our channel model has been adopted to overcome ISI and improve the system performance. It is plausible and convenient to utilize this impulse response model for performance analysis and system design of UWOC systems.