This paper proposes a novel control method based on the virtual AC/DC/AC conversion for the matrix converter. The virtual AC/DC/AC conversion method is a very simple strategy to control the input current and the output voltage for the matrix converter. There are two new topics proposed in this paper. Firstly, this paper proposes the minimum switching loss modulation on the virtual rectifier. In case of the proposed modulation, only two arms switching in the virtual rectifier using dc link current control by the virtual inverter can obtain clean sinusoidal input current. Secondly, a novel lean controlled carrier modulation on the virtual inverter is proposed. The leans of the triangle carrier are controlled by the duty ratio of the rectifier side pulse. The lean controlled carrier reduces harmonic distortion of the input current by avoiding interference between the rectifier control and the inverter control. These new proposals are confirmed by simulation and experimental results.