Memristor, the fourth basic circuit element, demonstrates obvious stochastic behaviors in both the static resistance states and the dynamic switching. In this work, a novel memristor-based true random number generator (MTRNG) is presented which leverages the stochastic property when switching a device between its binary states. Compared to conventional random number generators that require amplifiers or comparators with high complexity, the use of memristors significantly reduces the design cost: a basic MTRNG consists of only one memristor, six transistors, and one D Flip-flop. To maximize the entropy of the random bit generation, we further enhanced the design to a 2-branch scheme which can provide a uniform bit distribution. Our simulation results show that the proposed MTRNGs offer high operating speed and low power consumption: the reading clocks of the basic 1-branch and the enhanced 2-branch schemes can reach at 1.05GHz and 0.96GHz with power assumptions of 31.1μW and 80.3μW, respectively. Moreover, the zero-versus-one distributions and sampling rates of MTRNGs can be flexibly reconfigured by modulating the width and amplitude of the programming pulse applied on a memristor and therefore adjusting its switching probability between ON and OFF states.