We examine the muon g-2 anomaly based on new physics beyond the Standard Model. In particular, we concentrate on the correlations between the muon g-2 and the μ → eγ decay from effective operators, and use the μ → eγ experimental bound to constrain new physics. We explicitly show two possible methods to realize the model with a sizable muon g-2 and a small μ → eγ rate simultaneously.