A fluorosilicone rubber composition is provided comprising (A) a fluorosilicone gum having an aliphatic unsaturated monovalent hydrocarbon group content of 0.03-1 mol % based on the total of monovalent hydrocarbon groups and a residual alkali metal content of up to 20 ppm, (B) reinforcing silica having a specific surface area of 50-100 m2/g, and (C) an organic peroxide catalyst. The composition is molded into silicone rubber parts which are improved in compression set even after immersion in ε-caprolactam.