In this paper, we propose and experimentally demonstrate an auto-bias control scheme for stabilizing a lithium niobate (LN) Mach-Zehnder modulator (MZM) at any operating point along the power transmission curve. It is based on that the bias drift would change the operating point and result in varying the output optical average power of the Mach-Zehnder modulator and its first and second derivatives. The ratio of the first to the second derivative of the output optical average power is used in the proposed scheme as the key parameter. The experimental results show that the output optical average power of the LN MZM hardly changes at the desired operating point, and the maximum deviation of output optical average power is less than ±4%.