Motivated by an event excess in Higgs decay $h\rightarrow \mu \tau$ reported by the CMS experiment, we consider a general two Higgs doublet model (2HDM) which predicts the flavor violating phenomena beyond the standard model. Within the framework of the 2HDM, we show the scenario where the $\mu-\tau$ flavor violation can explain the anomaly of the muon anomalous magnetic moment as well as the CMS event excess in $h\rightarrow \mu\tau$. We discuss $\tau\rightarrow \mu \gamma$, the Michel parameters and lepton flavor non-universality in the $\tau$ decays $\tau \rightarrow l \nu \bar{\nu}~(l=e,\mu)$ as interesting predictions in this scenario.