The COMET Experiment at J-PARC aims to search for the lepton flavour violating (LFV) process of muon-to-electron conversion in a muonic atom, $\mu^{-}N \rightarrow \mathrm{e}^{-}N$, with a branching-ratio sensitivity of $6 \times 10^{-17}$ which is 4 orders of magnitude better than the present upper limit.

Complemental searches for two kinds of muon LFV decay modes, $\mu^{+} \rightarrow \mathrm{e}^{+}\gamma$ and $\mu^{-}N \rightarrow \mathrm{e}^{-}N$, are quite important in order to explore the parameter region predicted by the most well-motivated theoretical models beyond the Standard Model such as SUSY-GUT, seesaw, little-Higgs, extra-dimension, etc. MEG collaboration reported the latest result on $\mu^{+} \rightarrow \mathrm{e}^{+}\gamma$ search at PSI in Switzerland, and made a strong limit on new physics models, i.e. filling in the missing peace of muon LFV, $\mu^{-}N \rightarrow \mathrm{e}^{-}N$, will certainly play a very important role. The need for such an unprecedented sensitivity places several stringent requirements on both the muon beam and the detector system.

In order to realise the experiment effectively and efficiently, a staging approach to deployment is endorsed by the J-PARC Program Advisory Committee and KEK, and the “COMET Phase-I” experiment will commence its engineering runs in 2019. In Phase-I, a search for $\mu^{-}N \rightarrow \mathrm{e}^{-}N$ will be performed with an intermediate sensitivity which is 100 times better than the present upper limit.

In this contribution, prospects for COMET Phase-I and Phase-II both are presented in addition to the current status of construction of facility and detectors.