Underwater wireless optical communication (UWOC) is useful for transmitting data short distances in the ocean. In most cases, such devices are placed on underwater vehicles to make it easier to establish a communication link. However, the vehicle often works in dark water. Thus it needs a light emitting diode (LED) as an illuminant for its camera to observe the surroundings, but this is noise to the UWOC system. Although such noise could be eliminated by inserting an optical filter in the UWOC receiver, the effectiveness depends on the incident angle of light into the filter. Because the illumination distribution of LED is quite complicated, there are some special requirements for UWOC systems to eliminate such noise. First, we simulate the incident angle distribution of LED illumination noise into the receivers of a bidirectional UWOC system with the Monte Carlo method. Then we analyze its influence to design an UWOC system. The results show that the wavelength of UWOC should be shorter than that of the LED illuminant to make them work simultaneously. Under the condition that the noise can be eliminated effectively, the spectrum width of the communication signal and the optical filter should be wider to enlarge the receiving field. According to the theoretical conclusion, we experimentally demonstrate a half-duplex UWOC system with an LED illuminant in dark water, where the attenuation coefficient is about 0.20 m ^{− 1}. In the system, each terminal has a white LED illuminant with 6.01 W optical power, a blue LED illuminant with 7.72 W optical power, and a UWOC transmitter based on a purple LED with about 1.25 W optical power. The UWOC realized a 27.78 Mbps rate and 19 m distance when the illuminants were open. The proposed UWOC system and its design criteria are useful for UWOC applications.