The magnetic glass state has been proposed and studied in the ferromagnetic (FM) compounds undergoing the first-order FM-antiferromagnetic (AFM) transition. In this work, we have unequivocally demonstrated the occurrence of magnetic-glass-like transition during the field cooling process in the ferrimagnetic (FIM) Mn1.975Cr0.025Sb alloy showing a first-order FIM-AFM transition. The magnetic, resistance and relaxation studies characterize the formation of a nonergodic magnetic glass-like state at low temperature arising from the coexistence of AFM and kinetically arrested FIM phases above a critical applied field. The magnetic field-temperature (μ0H-T) phase diagram based on magnetic and resistance measurements further evidences the generality of onset of glassy behavior in the first-order magnetic transition materials, in which the transition temperature shifts strongly with increasing applied field.