A Dirac semimetal is a newly discovered electronic phase in condensed matter physics, which possesses promising properties for electronic applications, by sharing the same properties as a metal and semiconductor. These materials are composed of having a linear electronic band dispersion, high carrier mobility and ultrahigh magnetoresistance. Cadmium arsenide (Cd₃As₂) is a 3D Dirac semimetal which has gained attention in research studies. To study this material for such electronic device applications, high quality thin films are required for analysis. Molecular beam epitaxy (MBE), which is a low energetic deposition technique, is one of the best approaches to grow these thin films. We grew thin films using MBE, resulting in high quality on a lattice matched buffer layer with controlled thickness. An alloy of AlSb and InSb was used as an insulating lattice matched buffer layer between the Cd₃As₂ thin film and a GaSb substrate. X-ray diffraction data shows thin films are closely lattice matched with the Al0.4In0.6Sb buffer layer. Atomic force microscopy data shows a smooth surface morphology. Electron mobility of 8,050 cm²/V-s with low carrier density of 5×10¹¹ cm⁻² were obtained at 2 K. Ultimately, we grew the Cd₃As₂ thin film on a lattice matched substrate, which has similar mobility and lower carrier density than a previous Cd₃As₂ thin film grown on a lattice mismatched substrate, showing an improved quality of the Cd₃As₂ thin film.