MnBi2Te4 has attracted tremendous research interest recently as the first intrinsic antiferromagnetic (AF) topological insulator. It undergoes a long-range AF order at TN = 24 K accompanied with a cusp-like anomaly in the metallic resistivity. Here, we studied the effect of hydrostatic pressure on its electrical transport properties up to 12.5 GPa by using a cubic anvil cell apparatus. We find that TN determined from the resistivity anomaly first increases slightly with pressure and then decreases until vanished completely at ~7 GPa. Intriguingly, its resistivity rho(T) is enhanced gradually by pressure, and evolves from metallic to activated behavior as the AF order is suppressed. From the Hall resistivity measurements, we confirm that the n-type carriers dominate the transport properties and the carrier density is raised by pressure. In addition, the critical magnetic field Hc1 ~3.3 T at 0 GPa for the spin-flop transition to the canted AF state is found to increase to ~ 5 T and 7.5 T at 1 and 3 GPa. High-pressure XRD evidenced no structural transition up to 12.8 GPa. Based on the Hall resistivity results and first-principles calculations, we proposed that the intralayer direct AF interactions are strengthened by pressure and the competition between AF and FM interactions not only prevents long-range magnetic order but also promotes charge carrier localizations through enhance magnetic fluctuations at high pressures.