An electromagnetic calorimeter (ECAL) has been developed for the COMET experiment at J-PARC in Japan, which searches for muon-to-electron conversion of a charged lepton flavor violating process with a single event sensitivity of $10^{-17}$. The observation of this process forbidden in the standard model (SM) gives a clear evidence of new physics beyond the SM. The experiment aims at achieving a single event sensitivity of $10^{-17}$. The detector system consists of an upstream tracker and the ECAL. The ECAL is required to have an energy resolution < 5%, position resolution $< 1$ cm, and time resolution < 1 nsec at 105 MeV, the signal electrons energy. In order to satisfy those requirements, the ECAL consists of LYSO scintillating crystals. Several ECAL prototypes have been developed and evaluated. They have shown an excellent energy resolution of 4.2%, and position resolution of 7.6 mm at 105 MeV/c, and time resolution < 1 nsec, linearity within 0.5%, and particle identification efficiency > 90%. In this paper the detailed design and performance of the ECAL are described.