The invention discloses an FAM-B-methanol-gasoline-resistant low-temperature-resistant low-compressive-deformation ethylene-acrylate rubber material and a preparation method thereof, belonging to the technical field of rubber preparation. The preparation method comprises the following steps: sending 90-110 parts of ethylene-acrylate rubber, 1-4 parts of 4,4'-di(phenylisopropyl)diphenylamine, 0.2-1.4 parts of processing assistant 18D, 0.5-1.8 parts of stearic acid, 0.5-1.3 parts of processing assistant VAM, 0-130 parts of thermo-cracking carbon black N990, 0-70 parts of quick-extrusion carbon black N550 and 2-17 parts of softening and plasticizing agent TP-759 into a Banbury mixer, and banburying to obtain a master batch; and sending the master batch, 1.2-1.9 parts of crosslinking assistant HMDC-1 and 1-3 parts of vulcanizing agent into the Banbury mixer, carrying out secondary compounding, discharging the rubber when the temperature reaches 100 DEG C, and finally, carrying out molding, primary vulcanization and secondary vulcanization. The rubber material has the advantages of excellent FAM B methanol gasoline resistance, low temperature resistance and low compressive permanent deformation.