Muon cooling is an important technology for novel muon experiments involving muon acceleration such as the J-PARC muon g-2/EDM experiment, a muon microscope, and a muon collider. At J-PARC, the ultra-slow muon source, generated by laser ionization of thermal muonium in the vacuum, is under development. The emittance of the muon beam can be reduced by three orders of magnitude compared to the conventional muon beam through the re-acceleration of the ultra-slow muon. At the H2 area, one of the branches of the high-intensity pulsed muon beamline (H-line) at J-PARC, the designed flux of the ultra-slow muon source is an order of $10^5$/s, with completion projected for FY 2026. This paper provides the current status of muon cooling at J-PARC and its future prospects.