By means of density functional theory (DFT) computations and global minimum search using particle swarth optimization (PSO) method, we predicted three FeB6 monolayers, namely alpha-FeB6, beta-FeB6 and gamma-FeB6, which consist of the Fe(C)B-x (x = 6, 8) wheels with planar hypercoordinate Fe atoms locating at the center of six- Or eight-membered boron rings. In particular, the alpha-FeB6 sheet constructed, by Fe(C)B-8 motifs is the global minimum due to completely shared and well delocalized electrons. The two-dimensional (2D) boron networks are dramatically stabilized by the electron transfer from Fe atoms, and the FeB6 monolayers have pronounced stabilities. The alpha-FeB6 monolayer is metallic) while the beta-FeB6 and gamma-FeB6 sheets are semiconductors with indirect band gaps and significant visible-light absorptions. Besides the novel chemical bonding, the high feasibility for experimental realization, and unique electronic and optical properties, render them very welcome new members to the graphene-like materials family.