Recently, HAWC reported discovery of an extended TeV emission around the Geminga pulsar (so-called TeV halo), extended over a size of tens of parsecs. The importance of the discovery lies in that its implication for the existence of an unexpected inefficient diffusion zone in the local ISM that well traps cosmic-ray electron/positron within the TeV halo, and support of a dark matter origin of the cosmic-ray positron excess measured at Earth. I will show our analysis of the GeV gamma-ray data and X-ray data of the TeV halo, based on which we revisited the conclusion in the previous literature. Our study leads to a different picture of the cosmic-ray propagation in the local ISM and a different implication for the origin of the cosmic-ray positron excess.
