The anomalous magnetic moment of muon can be calculated in the Standard Model (SM) taking into account the quantum electrodynamics (QED), electroweak, and hadronic contributions, however, the current experimental results show a discrepancy with the theoretical expectation by more than 3$\sigma$. This may imply a presence of the New Physics, therefore, precision measurements of the muon anomaly is crucial. The latest experimental results were obtained by E821 at the Brookhaven National Laboratory (BNL) with an uncertainty of 0.54\,ppm, and its successor, Muon $g-2$ Experiment at the Fermi National Accelerator Laboratory (FNAL) is in operation to reduce the uncertainty. At the Japan Proton Accelerator Research Complex (J-PARC), another experiment for the precision measurement of the muon anomaly as well as the electric dipole moment of muon is being developed using a new experimental approach. Instead of using a storage ring with a magic momentum of muon as E821 and FNAL, a storage magnet with a three-dimensional injection of a reaccelerated thermal muon beam will be used. Since the experimental approaches are different, sources of important systematic uncertainties of the measurements are different, therefore, it is critical to obtain consistent results from the experiments. In this paper, experimental designs, progress, status, and future prospects are discussed.