The memristor has drawn the worldwide attention since it has been discovered at HP laboratory on 1 May 2008. Since then many researchers are taking efforts to find its applications in various areas. In this paper, we study the filter characteristics of first-order low pass and high pass filters employing memristor with a capacitor. The paper provides a comparative analysis between low pass and high pass filter circuits that utilizing ordinary resistor or memristor with a capacitor. The theoretical analyzes are verified with SPICE simulation results using a memristor SPICE model with nonlinear dopant drift and MATLAB environment. The effect of change of the input frequency and initial resistance value of memristor on the cut-off frequencies of the presented low pass and high pass filters are investigated. The memory effect of memristor is represented by simulation results.