The muon particle physics program at J-PARC will be mentioned, in
particular charged lepton flavor violation with muons. Muon to electron conversion in a muonic atom is a process of charged lepton flavor violation (CLFV). The COMET experiment aims to search for muon to electron conversion at J-PARC with single-event sensitivity of
3×10^{-17}. which is about 10,000 improvement over the current limit.
Recently the COMET experiment has taken a staged approach. COMET
Phase-I. as the first phase, aims at a single-event sensitivity of
3×10^{-15} with a partial part of the full muon beam line and a Phase-I dedicated detector in the order of about 10^{6} sec. The funds for COMET Phase-I has been approved as the supplemental budget, and the construction has started in 2013. The physics run is expected to start in 2018-9. The COMET Phase-II will follow immediately. In this talk, I will describe physics motivation of CLFV, and the details of COMET Phase-I / Phase-II together with the current status.