  This paper introduces a new approach to measure the muon magnetic moment
anomaly $a_{\mu} = (g-2)/2$, and the muon electric dipole moment (EDM)
$d_{\mu}$ at the J-PARC muon facility. The goal of our experiment is to measure
$a_{\mu}$ and $d_{\mu}$ using an independent method with a factor of 10 lower
muon momentum, and a factor of 20 smaller diameter storage-ring solenoid
compared with previous and ongoing muon $g-2$ experiments with unprecedented
quality of the storage magnetic field. Additional significant differences from
the present experimental method include a factor of 1,000 smaller transverse
emittance of the muon beam (reaccelerated thermal muon beam), its efficient
vertical injection into the solenoid, and tracking each decay positron from
muon decay to obtain its momentum vector. The precision goal for $a_{\mu}$ is
statistical uncertainty of 450 part per billion (ppb), similar to the present
experimental uncertainty, and a systematic uncertainty less than 70 ppb. The
goal for EDM is a sensitivity of $1.5\times 10^{-21}~e\cdot\mbox{cm}$.
