Provided is an aqueous binder for inorganic fibers, which is formaldehyde-free, has excellent strength, and is suitable for use under conditions of weakly acidic to weakly basic, and by which a cured product composed of the binder having excellent strength is obtained, and an thermal and/or acoustical insulation material made of inorganic fiber using the same. The thermal and/or acoustical insulation material is molded by using an aqueous hinder for inorganic fibers including: an acrylic resin with an acid value of 350 to 850 mgKOH/g; a crosslinking agent containing at least one dialkanolamine; and a curing accelerator, in which a molar ratio of the total number of the hydroxyl groups and imino groups in the crosslinking agent to the total number of carboxyl groups in the acrylic resin is 0.8:1 to 1.5:1, and in which pH of the hinder is adjusted to 6.0 to 8.0 with a volatile basic compound.