In a cooking process of a lignocellulose material, pulp yield can be improved at the same Kappa number and an effective alkali addition rate can be reduced at the same Kappa number.In a continuous cooking process making use of a digester, which includes therein, from a top toward a bottom of the digester, a top zone, an upper cooking zone, a lower cooking zone and a cooking/washing zone and also includes strainers provided at the bottom of the respective zones and wherein a cooking black liquor extracted from at least one of the strainers is discharged to outside a digestion system, a process for cooking a lignocellulose characterized by comprising feeding, upstream of the top of the digester, a first cooking liquor comprised of an alkaline cooking liquor having specified composition, feeding a second cooking liquor comprised of an alkaline cooking liquor made mainly of sodium hydroxide to the upper cooking zone, and feeding a third cooking liquor comprised of an alkaline cooking liquor similar to the second cooking liquor to the cooking/washing zone.