A process for producing a stable acidic aqueous alumina sol containing 50 to 300 nm of elongate secondary particles which are elongated in only one plane and formed by edge-to-edge coagulation of rectangular plate-like primary particles having a length of one side of 10 to 30 nm when observed through an electron microscope, the process comprises the steps of:(A) adding an alkali to an aqueous alumina sol containing fibrous colloidal particles of an amorphous alumina hydrate to produce a reaction mixture having a pH of 9 to 12,(B) subjecting the reaction mixture obtained in the step (A) to a hydrothermal treatment at a temperature of 110 to 250.degree. C. to produce an aqueous suspension containing an alumina hydrate having a boehmite structure, and(C) desalting the aqueous suspension obtained in the step (B) by adding water and an acid by ultrafiltration to form an acidic aqueous alumina sol having a pH of 3 to 6.