Long pulse beam accelerations with MeV-class hydrogen negative ions have been demonstrated by using Multi-Aperture and Multi-Grid (MAMuG) accelerators toward high power neutral beam injector (NBI) required in JT-60SA and ITER. This paper reports that pulse duration of the ITER-relevant current density of hydrogen negative ion beams at 1 MeV has been successfully extended from 0.4 s to 60 s by using a prototype five-stage MAMuG accelerator for ITER. The key for this achievement is to reduce the power loadings due to a direct interception of negative ions and secondary electrons on the acceleration grid. The extraction grid has been modified to optimize the beam optics and to control the beam directions. The acceleration grid has been modified to suppress the secondary electron generations. For these modifications, three-dimensional beam analyses including the collision process and the detail configuration of the accelerator have been improved step by step with the experimental validation. Finally, the total power loading on the acceleration grids has been successfully reduced to less than 10 % of the total beam acceleration power. As the result, 0.97 MeV, 190 A/m$^2$ negative ion beam was achieved for 60 s without breakdown, which was comparable to the ITER requirement of 1 MeV, 200 A/m$^2$. This long pulse beam acceleration with the ITER-relevant beam contributes to assure the 1 MeV accelerator for the ITER NBI.