There has been an upsurge in the discovery of topological quantum materials, where various topological insulators and semimetals have been theoretically predicted and experimentally observed. However, only very few of them contains silicon, the most widely used element in electronic industry. Recently, ternary compound CaAl2Si2 has been predicted to be a topological Dirac semimetal, hosting Lorentz-symmetry-violating quasiparticles with a strongly tilted conical band dispersion. In this work, by using high-resolution angle-resolved photoemission spectroscopy (ARPES), we investigated the comprehensive electronic structure of CaAl2Si2. A pair of topological Dirac crossings is observed along the kz direction, in good agreement with the ab initio calculations, confirming the topological Dirac semimetal nature of the compound. Our study expands the topological material family on Si-containing compounds, which have great application potential in realizing low-cost, nontoxic electronic device with topological quantum states.