A process for selectively hydroesterifying only a vinyl group of (1-arylethenyl)vinylbenzene by reacting it with carbon monoxide and water or a lower alcohol in the presence of a noble metal complex catalyst at a temperature of 40 to 200°C and a carbon monoxide pressure of 20 to 700 Kg/cm2 to thereby prepare alpha-((1-arylethenyl)propionic acid or its alkyl ester. The starting material to be hydroesterified may be a mixture of the above vinylbenzene with 1,1-di(substituted aryl)ethylene not substituted by a vinyl group.