We study the CDF W -mass, muon g − 2, and dark matter observables in a local U (1) Lµ−Lτ model in which the new particles include three vector-like leptons (E 1 , E 2 , N ), a new gauge boson Z , a scalar S (breaking U (1) Lµ−Lτ ), a scalar dark matter X I and its partner X R . We find thatof left (right)-handed fields of vector-like leptons. A large mass splitting between E 1 and E 2 is favored when the differences between s L and s R becomes small. The muon g − 2 anomaly can be simultaneously explained for appropriate difference between s L (m E 1 ) and s R (m E 2 ), and some regions are excluded by the diphoton signal data of the 125 GeV Higgs. Combined with the CDF W -mass, muon g − 2 anomaly and other relevant constraints, the correct dark matter relic density is mainly obtained in two different scenarios: (i) X I X I → Z Z , SS for m Z (m S ) < m X I and (ii) the co-annihilation processes for min(m E 1 , m E 2 , m N , m X R ) closed to m X I . Finally, we use the direct searches for 2 + E miss T event at the LHC to constrain the model, and show the allowed mass ranges of the vector-like leptons and dark matter.