An experiment to measure the anomalous magnetic moment ( \(g-2\) ) and the electric dipole moment (EDM) of the muon is being prepared at J-PARC. The experimental average of the muon \(g-2\) , combining the latest Fermilab E989 measurement shows a discrepancy of more than five standard deviations from the Standard Model prediction. The J-PARC experiment uses different techniques from Fermilab E989, such as a low-emittance muon beam, a compact storage ring without electric focusing, and track detection of decay positrons. The experiment is scheduled to begin commissioning in 2029 JFY, and the development and implementation of experimental instruments, as well as the design and construction of the facility, are currently underway. Recently, the first-stage acceleration of cooled muons was successfully demonstrated at J-PARC. The current status of the experiment is described in this document.