A filter is required to remove the high frequency switching ripple present in the input current of the matrix converter. A design procedure for a single stage L-C filter is presented in this paper based on the specifications of allowable ripple in the grid current and distortion in the input voltage of the matrix converter. This requires an accurate estimation of the ripple component present in input line current. An analytical method to estimate this switching ripple is presented, and the converter is modeled for fundamental frequency. A damping resistor is designed to damp the oscillations due to LC resonance, with minimum power loss. The converter is simulated in MATLAB/Simulink and the filter design results are verified.