It is well known that there is a discrepancy between observed value and the SM prediction of the muon anomalous magnetic moment (muon g-2). The discrepancy is more than 3 sigma, and thus it can be regarded as an evidence of physics beyond the standard model (SM). Two Higgs doublet model (2HDM) is a model simply extended from the SM and have been widely studied. There are several variation on the model. In this talk, I focus on the lepton specific 2HDM (type-X 2HDM) as a solution of the muon g-2. Thanks to lepton specific properties of the new particles, the model can explain the muon g-2 although there are severe constraints from flavour physics, especially from the lepton flavour universality. I also discuss phenomenology of this model at the LHC.