This paper proposes a method to study the transmission characteristics of ultraviolet turbulent channels, by considering the variation of atmospheric refractive index structure parameters along transmission paths. This method is adopted in a Monte Carlo simulation to analyze the transmission characteristics of ultraviolet light when the communication nodes are mobile. The analysis focuses on the influence of the moving speed and direction of the receiver on path loss under long-distance and atmospheric turbulence conditions. The simulation results show that, when the altitude increases, atmospheric refractive index structure parameters show a decreasing trend, and the path loss of the system decreases. With or without turbulence, when the receiver moves away from the transmitter in a horizontal plane, the received signal strength always decreases as the moving speed increases; and vice versa. When the receiver moves along the vertical axis, the signal strength increases as the moving speed increases. With the presence of atmospheric turbulence, the received signal strength attenuates significantly, compared with the case with no turbulence. When the receiver moves along the vertical axis, the path loss is higher compared with the situation when the receiver moves on the horizontal plane.