The invention discloses a matrix converter comprising a source damping filtering unit. The matrix converter comprises an input power source, an LC input filtering unit, a switch matrix and a microprocessing unit. Currents provided by the input power source are input to a load successively through the LC input filtering unit and the switch matrix, the microprocessing unit, through control over the resonance damping of an LC filter, controls input current waveforms of the LC filter so as to obtain expected output voltages, and according to the expected output voltages, distributes pulses to each switch tube in the switch matrix to control the work state of each switch tube in the switch matrix. The invention also provides a control method of the matrix converter comprising the source damping filtering unit. The dynamic characteristic is improved, the power supply current harmonic wave content can be reduced, a power supply side is enabled to be always close to a unit power factor, and the efficiency of the matrix converter is improved. At the same time, resonance appearing in the LC filter is effectively inhibited, the total harmonic wave distortion rate of power supply currents is reduced, and the influence exerted by the matrix converter on a power network is decreased.