The possible candidates of S-wave dibaryons with various strange numbers are studied under the chiral SU(3) quark model. It is shown that there are three types of baryon–baryon bound states. The states of the first type are called deuteron-like states. If chiral fields can provide enough attraction between interacting baryons, these systems, such as [ΞΩ−Ξ∗Ω](1,1/2), [ΞΞ](0,1), [NΩ](2,1/2) would be weakly bound. The states of the second type such as [Σ∗Δ](0,5/2), [Σ∗Δ](3,1/2), [ΔΔ](0,3) and [ΔΔ](3,0) are named as ΔΔ-like states. Due to the highly symmetric character in orbital space, these systems could be relatively deeply bound, but the strong decay modes of composed baryons cause the widths of the states much broader. The states of the third type are entitled as ΩΩ-like states. Due to the same symmetry character shown in the systems of the second type and the only weak decay mode of composed baryons, for instance in [ΩΩ](0,0), or at most one strong decay mode of composed baryons, for example in [Ξ∗Ω](0,1/2), these states are deeply bound states with narrow widths. The states of latter two types are most interesting new dibaryon states and should be carefully investigated both theoretically and experimentally.