This paper presents a matrix converter design for achieving maximum power density using a SiC device based on a front loading design. To design the matrix converter to achieve maximum power density, the conduction loss and the switching loss of the matrix converter are theoretically derived and validated by simulation and experiment. Based on these formulas, the relationship between the efficiency and power density are revealed by using a Pareto-front curve in order to solve the trade-off problem between the power density and the efficiency. Moreover, in order to promote the widespread use of the matrix converter instead of a BTB system, it is quantitatively evaluated that the power density in the matrix converter is increased by 4.19 kW/dm 3 in comparison to the BTB system. Moreover, the power density of the matrix converter that uses a SiC-MOSFET (ROHM) as the switching device with natural air cooling is 95.0% (2.1 kW/dm 3 ) of the calculated maximum power density. Thus, the power density of the matrix converter is improved by 57.5% by the maximum power density design method. Based on the results, the design method for a high power density AC-AC direct converter is established according to the requisite specifications.Index Terms-Front loading design, loss analysis, matrix converter, maximum power density design, Pareto-front curve