Recent measurement of the muon anomalous magnetic moment, $a_{\mu} = (g_{\mu}-2)/2$,
with a precision of 0.46~ppm at the Fermilab National Accelerator Laboratory (FNAL)
confirmed the anomaly observed at the Brookhaven National Laboratory (BNL) more than a decade.
Now the tension between the measurements and the Standard Model (SM) prediction
becomes 4.2 standard deviations.
Though this may imply existence of new physics beyond SM,
it should be verified with other measurements.
The J-PARC experiment aims to measure $a_{\mu}$ and the electric dipole moment (EDM) in a completely different way than the BNL and FNAL experiments, by using a low-emittance muon beam
realized by acceleration of the thermal muons.
This paper reports the current status of each experimental component.