The recent research progress on molecular beam epitaxy growth of HgCdTe on Si substrate is reported. Based on the fabrication technology of MW HgCdTe and SW HgCdTe on Si substrate,the fabrication technology of molecular beam epitaxy growth of SW/MW-HgCdTe on Si based substrate was developed. Through on-line monitoring of RHEED,the fabrication technology for SW/MW-HgCdTe growth on Si substrate was optimized. With this technology,high quality SW/MW-HgCdTe wafers were obtained.