The muon anomalous magnetic moment $(g-2)_{\mu}$ and electric dipole moment are sensitive to new physics beyond Standard Model (SM).
There is a discrepancy between
the $(g-2)_{\mu}$ measured by E821 collaboration at Brookhaven National Laboratory (BNL)
and the SM prediction at more than $3 \sigma$ level.
Our goal is to measure $(g-2)_{\mu}$ with a precision of 0.1 parts per million
and search for electric dipole moment with a sensitivity of $10^{-21} e \cdot$cm, respectively.
To achieve unprecedented precision, we utilize high intensity proton beam at J-PARC
and newly developed technique of ultra-cold muon beam from muonium,
which is completely different and independent from methods used at BNL and Fermi National Accelerator Laboratory.
We report our experimental approaches and current status of each component of our experiment.