The impact of hydrostatic pressure up to 1.2 GPa on the critical current density (J c ) and the nature of the pinning mechanism in MgB 2 have been investigated within the framework of the collective theory. We found that the hydrostatic pressure can induce a transition from the regime where pinning is controlled by spatial variation in the critical transition temperature (δT c ) to the regime controlled by spatial variation in the mean free path (δℓ). Furthermore, T c and low field J c are slightly reduced, although the J c drops more quickly at high fields than at ambient pressure. We found that the pressure raises the anisotropy and reduces the coherence length, resulting in weak interaction of the vortex cores with the pinning centres. Moreover, the hydrostatic pressure can reduce the density of states [N s (E)], which, in turn, leads to a reduction in the critical temperature from 39.7 K at P = 0 GPa to 37.7 K at P = 1.2 GPa.Magnesium diboride (MgB 2 ) is a promising superconducting material which can replace conventional low critical temperature (T c ) superconductors in practical applications, due to its relatively high T c of 39 K, strongly linked grains, rich multiple band structure, low fabrication cost, and especially, its high critical current density (J c ) values of 10 5 -10 6 A/cm 2 [1-9]. Numerous studies have been carried out in order to understand the vortex-pinning mechanisms in more detail, which have led to real progress regarding the improvement of J c . There are two predominant mechanisms, c pinning, which is associated with spatial fluctuations of the T c , and ℓ pinning, associated with charge carrier mean free path (ℓ) fluctuations [10][11][12][13][14].Very recently, our team have found that hydrostatic pressure is a most effective approach to enhance J c significantly in iron based superconductors, as the pressure can induce more point pinning centres and also affect the pinning mechanism [15]. Therefore, it is natural to investigate the impact of hydrostatic pressure on J c and flux pinning mechanisms in MgB 2 . Previous studies have shown that pressure of 1 GPa can reduce T c , but only by less than 2 K in MgB 2 . This is a very insignificant reduction as compared to the other approaches (i.e. chemical doping and irradiation) which are mainly used for J c enhancement [16]. For instance, chemical doping can significantly enhance J c in MgB 2 , but with a considerable degradation of T c ; carbon doping can reduce T c from 39 K to nearly as low as 10 K, for carbon content up to 20% [17][18][19][20][21][22]. Similarly, the irradiation method can improve J c in MgB 2 , but it reduces T c values significantly (by more than 20 K in some cases) [23][24][25][26][27]. Correspondingly, the chemical doping and irradiation methods can also change the nature of the pinning mechanism in MgB 2 [24,[28][29][30]. The determination of J c and the flux pinning mechanism under hydrostatic pressure is also an important step to probe the mechanism of superconductivity in more detail in MgB 2 . It is very i...