This paper presents a single-phase AC-AC matrix converter as a frequency converter. Due to continuous increase in the use of electronics converters like AC- AC, AC- DC, DC – AC and DC-DC, there is always a thrust to develop a converter, which generates lesser harmonics, minimum switching losses and high quality desired waveforms across output and input. It stimulates the researchers to innovate new ideas to minimize these effects. In this paper, the focus is to design and Implementation of Matrix Converter (MC) for frequency changing applications .A simple PWM mechanism is proposed to design a mathematical model of single phase Matrix Converter. There is no DC link between rectifier and inverter stage which add up some efficient properties like compact design, bidirectional current flow capabilities. A suitable commutation technique is analyzed. Simulation work is done in MATLAB Simulink environment and comparison with mathematical results is presented.