In high-quality c-axis-oriented MgB2 thin films, we observed high critical current densities (Jc) of ∼ 16 MA/cm 2 at 15 K under self fields comparable to, and exceeding, those of cuprate hightemperature superconductors. The extrapolated value of Jc at 5 K was estimated to be ∼ 40 MA/cm 2 . At a magnetic field of 5 T, a Jc of ∼ 0.1 MA/cm 2 was detected at 15 K, suggesting that this compound would be a very promising candidate for practical applications at high temperature and lower power consumption. The vortex-glass phase is considered to be a possible explanation for the observed high current carrying capability.The recent discovery of the binary metallic MgB 2 superconductor [1] with a remarkably high transition temperature T c = 39 K has attracted great interest in both basic scientific [2][3][4][5][6] and practical applications [7][8][9][10][11][12][13][14]. This new compound is expected to be useful for superconducting magnets and microelectronic devices at low cost because its transition temperature is 2 − 4 times higher than those of conventional metallic superconductors such as Nb 3 Sn and Nb-Ti alloy. The strongly linked nature of the intergrains [7] with a high charge carrier density [6] in this material is a further indication of its possible use in technological applications. Recently, an upper critical field, H c2 (0), of 29 ∼ 39 T [8,9], which was much higher than previously reported, was observed, suggesting that MgB 2 should be of considerable use for practical application in superconducting solenoids using mechanical cryocoolers, such as closed-cycle refrigerator. In addition to the higher T c and H c2 in MgB 2 , the magnitude of the critical current density is a very important factor for practical applications. For example, if a superconducting wire carries a high electric power, the size of the cryogenic system can be reduced considerably so that the system can operate with lower power consumption. Indeed, the successful fabrication of Fe-clad MgB 2 tape has been reported [10]. This tape showed a J c of 1.6 × 10 4 A/cm 2 at 29.5 K under 1 T, which is encouraging for practical application of MgB 2 .In order to explain the nature of the vortex state in strong magnetic field for cuprate high-T c superconductors (HTS), Fisher et al. [15] proposed the theory of vortex-glass superconductivity by considering both the pinning and the collective effects of vortex lines. According to this theory, a diverging vortex glass correlation length (ξ) near the vortex-glass transition (T g ) can be described by ξ ∼ |T − T g | −ν and a correlation time scale ξ z , where ν is a static exponent and z is a dynamic exponent; thus, I − V curves can be expressed by universal scaling functions. For HTS, experimental evidence of a vortex glass phase has been reported [16]. Moreover, a vortex-glass transition was observed in an untwinned single crystal of YBa 2 Cu 3 O 7 after inducing a sufficiently high density of pinning centers, suggesting that a vortexglass phase may be one origin of the high J c [17].In this Letter,...