The hysteretic dependences of the magnetoresistance of porous (38% of the theoretical density) granular high-temperature superconductor (HTSC) Bi 1.8 Pb 0.3 Sr 1.9 Ca 2 Cu 3 O x have been analyzed in the model of the effective intergranular field. This effective field has been defined by the superposition of the external field and the field induced by magnetic moments of superconducting grains. The magnetic flux compression in an intergranular medium, characterized by the effective field, controls the hysteretic behavior of the magnetoresistance. It has been found that the magnetoresistance hysteresis width for the studied porous HTSC depends on the transport current, in contrast to the superconductor of the same composition with high physical density (more than 90% of the theoretical value). For a porous superconductor, a significant current concentration occurs in the region of the grain boundaries, which is caused by features of its microstructure. A current-induced increase in the effective boundary length results in a decrease in the flux compression, a decrease in the effective field in the intergranular medium, and a magnetoresistance hysteresis narrowing with increasing current.