Memristor, regarded as the new fourth fundamental circuit element by many, is also being considered for analog applications. It is expected that analog filters with memristors will provide some characteristics which cannot be mimicked by resistors. In this study, memristor-based low-pass and high-pass filters are analyzed and their performance demonstrated with simulations in time and frequency domains. Saturation of the memristor in the memristor-based filters at low frequencies and distortion resulting from it are observed. Also gain and total harmonic distortion of the filters as a function of frequency are given. The results obtained in this work can be used to design, memristor-based low-pass and high-pass filters.