In this study, mathematical models of a novel mechanism, rhombic-drive, for a two-stroke, spark ignition (SI) engine, and a two-stroke SI engine with a conventional slider-crank mechanism were performed in MATLAB software. Their performances were compared with kinematic and thermodynamic analyses. Mathematical model was conducted according to real cycle approach and some of the operating parameters such as compression ratio, swept volume, heat release time, and lambda were kept identical for both engines. Pressure, volume, temperature, heat release, heat transfer coefficient, work, piston speed, and acceleration changes were examined. Maximum in-cylinder pressure was taken at 222 degrees CA with 4,188 kPa for rhombic-drive engine while 190 degrees CA with 4,003 kPa for slider-crank mechanism engine and maximum temperature was only 39 K higher for rhombic-drive mechanism engine. Theoretical thermal efficiencies of rhombic-drive and slider-crank mechanism were 31.14% and 31.87%, respectively. Effective power of rhombic-drive mechanism engine was 2.12 kW, whereas slider-crank mechanism engine was 2.17 kW. Mechanical efficiency of rhombic-drive engine was obtained 85.89%, while this was only 86.21% for slider-crank mechanism engine.