Asystematic study of 32 honeycomb monolayer II-VI semiconductors is carried out by first-principles methods. While none of the two-dimensional (2D) structures can be energetically stable, it appears that BeO, MgO, CaO, ZnO, CdO, CaS, SrS, SrSe, BaTe, and HgTe honeycomb monolayers have a good dynamic stability. The stability of the five oxides is consistent with the work published by Zhuang et al. [Appl. Phys. Lett. 103, 212102 (2013)]. The rest of the compounds in the form of honeycomb are dynamically unstable, revealed by phonon calculations. In addition, according to the molecular dynamic (MD) simulation evolution from these unstable candidates, we also find two extra monolayers dynamically stable, which are tetragonal BaS [P4/nmm(129)] and orthorhombic HgS [P21/m(11)]. The honeycomb monolayers exist in the form of either a planar perfect honeycomb or a low-buckled 2D layer, all of which possess a band gap and most of them are in the ultraviolet region. Interestingly, the dynamically stable SrSe has a gap near visible light, and displays exotic electronic properties with a flat top of the valence band, and hence has a strong spin polarization upon hole doping. The honeycomb HgTe has recently been reported to achieve a topological nontrivial phase under appropriate in-plane tensile strain and spin-orbital coupling (SOC) [J. Li et al., arXiv:1412.2528]. Some II-VI partners with less than 5% lattice mismatch may be used to design novel 2D heterojunction devices. If synthesized, potential applications of these 2D II-VI families could include optoelectronics, spintronics, and strong correlated electronics.