In this work, a memristor based low-pass filter topology in which a memristor is placed as the input element and a capacitor is placed as the negative feedback element to an inverting op-amp is examined. The memristor provides adjustable gain characteristic to the filter. Analytical solution of the filter is obtained its output voltage, the memristor current, and the capacitor voltage are found as a function of time. To obtain the filter small-signal model and examine its frequency behavior, Maclaurin series expansion for the output voltage is performed. Time and frequency domain simulations of the filter are done using both small signal and dynamic models of the filter. The frequency domain gain and THD characteristic of the filter are also obtained using both of the models. Simulation results of both of the models are compared. It is shown that the small signal model is able to predict the filter behavior accurately for small signals. It has been also found that, for this topology at low frequencies, the input signal magnitude should be limited for a low distortion.