Considering the competition for oceanic resources among different nations, Underwater Wireless Communication (UWC) technology has a lot of potential for development. As compared to its traditional counterparts, namely underwater acoustic communication and radio frequency communication, Underwater Wireless Optical Communication (UWOC) has many advantages, such as a strong information-carrying capacity, a faster communication rate, and good confidentiality, which can better suit the practical communication requirements of high-speed and large-capacity, lower implementation costs, and lower time latency in underwater wireless communication. The effects of the UWOC channel on the received laser pulse are typically categorized into the signal power attenuation caused by absorption, scattering, and the light intensity scintillation caused by oceanic turbulence, which leads to a decline in the transmission performance (bit error rate) of the UWOC system. The most widely used turbulence channel models are only suitable for a specific turbulence state. In order to further analyze the signal characteristics and system performance of the UWOC system of the Offset Quadrature Phase Shift Keying (OQPSK) modulation under the common action of turbulence channel and attenuation channel, this paper uses the Exponential Generalized Gamma (EGG) turbulence distribution model, which is more consistent with real oceanic channel characteristics. We obtain the turbulent random noises utilizing the acceptance-rejection sampling algorithm and further establish a composite channel model taking into account the attenuation channel, turbulence channel, and the Additive White Gaussian Noise (AWGN). In addition, according to the waveform of simulating signal, varying turbulence noise parameters, system noise parameters, and attenuation channel parameters, we analyze the average Bit Error Rate (BER) characteristics of the OQPSK modulation in the UWOC system. The simulation results show that the signal waveform does not change when it passes through the attenuation channel, but the amplitude is severely attenuated; the signal envelope passing through the turbulence channel changes with time, and the speed of signal amplitude change is negatively correlated with the turbulence coherence time; the signal waveform passing through the composite channel is distorted nonlinearly. For strong oceanic turbulence of the scintillation index ${\sigma }_{\mathrm{I}}^{\mathrm{2}}=\mathrm{2}$, the performance of analog signals with carrier characteristics is better than the performance of the digital signal, where as compared to the Binary Phase Shift Keying (BPSK), the SNR gain of OQPSK is rough by 3 dB. For weak oceanic turbulence of the scintillation index ${\sigma }_{\mathrm{I}}^{\mathrm{2}}=\mathrm{0.2}$ with a water quality attenuation coefficient of $c=\mathrm{0.151}$ m^-1, the OQPSK system can achieve reliable communication of 50 meters at an average BER of ${\mathrm{10}}^{-\mathrm{3}}$ when the SNR is 20 dB. Under the same parameter of oceanic turbulence channel, the BER decreases linearly with the increases of the communication distance. At the same time, the quality of seawater has a great influence on the average BER of the UWOC system. In the weak oceanic turbulence channel of ${\sigma }_{\mathrm{I}}^{\mathrm{2}}=\mathrm{0.2}$ and turbulence coherence time ${\tau }_{\mathrm{0}}=\mathrm{10}$ ms, the UWOC system with the OQPSK modulation can achieve reliable communication of 40 meters at the average BER below ${\mathrm{10}}^{-\mathrm{3}}$ by increasing the SNR in the case of pure ocean water or clear ocean water, but it is noticed that the system with the OQPSK modulation can hardly achieve effective communication in the coastal ocean water.