A MgB 2 superconducting bulk has a promising potential as a quasi-permanent magnet. In this paper, we have performed pulsed-field magnetization (PFM) at T s = 14-20 K for MgB 2 superconducting bulks with a higher critical current density J c (B) fabricated by hot isostatic pressing. During PFM, a flux jump frequently took place, and trapped field B z decreased in the disk-shaped bulks for a higher magnetic field application. However, in the cylindrical bulk with identical J c (B) characteristics, the flux jump was avoided, and a maximum trapped field of B z = 0.81 T was obtained at 14 K, which is a record-high trapped field in a MgB 2 bulk by PFM. The electromagnetic and thermal instability was discussed using conventional relations to avoid the flux jump and to enhance the trapped field on the MgB 2 bulks with higher J c (B), higher thermal conductivity, and lower specific heat.Index Terms-Critical current density, flux jump, MgB 2 bulk magnet, pulsed-field magnetization (PFM), thermal and electromagnetic stability.