A composition for a sizing agent comprising (a) 70-99.9 wt. % of a substituted alkyl succinic anhydride or a substituted alkenyl succinic anhydride or a mixture of these succinic anhydrides, and (b) 0.1-30 wt. % of phosphates of polyoxyethylene alkyl ether esters or phosphates of polyoxyethylene alkyl aryl ether esters of a mixture of these phosphate esters and a process for using the composition by dispersing the composition, adding the produced aqueous dispersion to pulse slurry of paper making material, and making the paper. This composition for the sizing agent has excellent storage stability and underwater self-emulsion, and accordingly exhibits excellent sizing effect and provides paper having an excellent sizing effect.