Two-dimensional monolayer materials, with thicknesses of up to several atoms, can be obtained from almost every layer-structured material. It is believed that the catalogs of known 2D materials are almost complete, with fewer new graphene-like materials being discovered. Here, we report 2D graphene-like monolayers from monoxides such as BeO, MgO, CaO, SrO, BaO, and rock-salt structured monochlorides such as LiCl, and NaCl using first-principle calculations. Two-dimensional materials containing d-orbital atoms such as HfO, CdO, and AgCl are predicted. Adopting the same strategy, 2D graphene-like monolayers from mononitrides such as scandium nitride (ScN) and monoselenides such as cadmium selenide (CdSe) are discovered. Stress engineering is found to help stabilize 2D monolayers, through canceling the imaginary frequency of phonon dispersion relation. These 2D monolayers show high dynamic, thermal, kinetic, and mechanic stabilities due to atomic hybridization, and electronic delocalization. Significance Since the discovery of graphene in 2004, 2D materials have sparked tremendous interest due to their fascinating optical, mechanical, and electronic properties, and their potential in catalysis, optoelectronic devices, energy storage, and conversion. After experimental and theoretical studies mainly focused on atomically thin nanomaterials with layered structures, the whole family of 2D materials is almost complete, and recently few new graphene-like materials were reported. Here, we report the discovery of graphene-like mononitrides, monoxides, monochlorides, and monoselenide monolayers, which have shown high dynamic, thermal, kinetic, and mechanic stabilities.