To handle the significant light emitting diode (LED) nonlinearity clipping distortion problem in asymmetrically clipped optical orthogonal frequency division multiplexing (ACO-OFDM) based visible light communication systems, an optimal power allocation method for reducing the clipping distortion is proposed. The LED nonlinear clipping distortion of the system is analyzed based on the clipping process model that original signal directly addes nonlinear clipping distortion components. The effective signal to noise ratio (SNR) is defined to measure the clipping distortion, and the clipping distortion analysis is converted into SNR analysis. Finally, the optimal bias signal and ACO-OFDM signal power allocation under optical power constraints based on the principle of effective SNR optimum are proposed. Simulation results show that the channel noise dominants at low channel SNR value while clipping distortion dominates at high channel SNR value. Bit error rate (BER) is greater than 10-2 even the channel SNR value beyond 40 dB if the bias power is selected as the minimum output power limit value of LED without considering, while optimal power allocation can effectively reduce the LED nonlinear clipping distortion to improve the BER performance. Channel SNR values of 24 dB and 27 dB are enough to insure that BER is below 10-3 under the optical power constraints of 200 mW and 250 mW, respectively.