The present invention relates to an anhydrous composition in aerosol form comprising, in particular in a physiologically acceptable medium: a) an oily phase comprising i) at least one volatile oil, and ii) at least one nonvolatile hydrocarbon-based oil, and iii) at least one phenyl silicone, and b) at least one antiperspirant active agent chosen from aluminum and/or zirconium salts or complexes, c) at least one water-insoluble film-forming block ethylenic polymer d) at least one propellant. The invention also relates to a cosmetic process for treating human perspiration, and optionally the body odors associated with human perspiration, especially underarm odors, comprising the application of said composition to a surface of the skin.