This paper proposes a Gaussian behavior model to describe the LED memoryless nonlinearity of voltage-to-optical power (V-P) conversion process. The production mechanism of LED memoryless nonlinearity is analyzed. A serials of experiments on voltage-current-optical power (V-I-P) characteristics of different bands' LEDs are conducted. It is shown that the LED memoryless nonlinearity mainly exist in the low bias-voltage area and high injection current area. What's more, such a LED V-P process's nonlinear behavior appears to be described by Gaussian function with a high fitting degree. Based on the Gaussian nonlinear behavior model and its inverse function, a direct pre-distortion method is proposed to mitigate the memoryless nonlinearity of visible light communication system.