The muon linac is planned at the Japan Proton Accelerator Research Complex (J-PARC) for the precision measurement of the muon dipole moments. However, the muon acceleration with an radio-frequency (RF) accelerator was not carried out yet. Then, the first muon RF acceleration experiment using an radio-frequency quadrupole (RFQ) linac was carried out in the J-PARC. The incident positive muon was cooled using the production of the negative muonium ion (Mu-) before the accelaration. Subsequently, the Mu- was accelerated to 89 keV with the RFQ. Thanks to the pulsed muon beam in the J-PARC, the accelerated Mu- was clearly identified with the Time-Of-Flight measurement after the momentum selection with the bending magnet. The measured event rate of the accelerated Mu- was consistent with the expectation using the simulation and the result of the Mu- production experiment as the preparatory experiment of the acceleration experiment. The first muon RF acceleration was successful.