Recent b→sll anomalies may imply the existence of a new Z′ boson with left-handed Z′bs and Z′μμ couplings. Such a Z′ may be directly observed at LHC via bs→Z′→μ+μ-, and its relevance to b→sll may be studied by searching for the process gs→Z′b→μ+μ-b. In this paper, we analyze the capability of the 14 TeV LHC to observe the Z′ in the μ+μ- and μ+μ-b modes based on an effective model with major phenomenological constraints imposed. We find that both modes can be discovered with 3000 fb-1 data if the Z′bs coupling saturates the latest Bs-Bs mixing limit from UTfit at around 2σ. Besides, a tiny right-handed Z′bs coupling, if it exists, opens up the possibility of a relatively large left-handed counterpart, due to cancellation in the Bs-Bs mixing amplitude. In this case, we show that even a data sample of O(100) fb-1 would enable discovery of both modes. We further study the impact of a Z′bb coupling as large as the Z′bs coupling. This scenario enables discovery of the Z′ in both modes with milder effects on the Bs-Bs mixing, but obscures the relevance of the Z′ to b→sll. Discrimination between the Z′bs and Z′bb couplings may come from the production cross section for the Z′bb final state. However, we do not find the prospect for this to be promising.