A continuous process for production of cellulose pulp from grass-like plant feedstock, comprising the steps of: (i) preparing the grass-like plant feedstock by comminuting to produce a feedstock with longitudinal size distributed from 1.5-30 cm and diameter of 0.5-15 mm, and with removed fine dusty particles by dedusting of said feedstock with fan; (ii) continuous digestion of a grass-like dust-free plant feedstock prepared in step (i) in a digester formed as a vertical column internally having only smooth side walls; where dust-free grass-like plant feedstock is continuously fed directly on the top of the said digester via conveyor; characterized by that, - in parallel with said dust-free feedstock top-feeding, the chemicals for digestion selected from the group consisting of NaOH and NaCl or Na 2 SO 3, fresh water, regenerated water, and steam are introduced continuously on the top of said digester; maintaining the digestion temperature from 70-100 °C and average composition of thus formed suspension during said continuous digestion within the following ranges: (a) 0.9-1.5% w/w of NaOH; (b) 0.15-0.4% w/w of NaCl or Na 2 SO 3; and (c) 15-18% w/w of grass-like plant feedstock; where concentrations of ingredients being calculated on the weight of the liquid phase; - where dissolution of noncellulosic substances from the grass-like plant feedstock is performed during the mass transfer from the top to the bottom of the said digester performed only by the gravity that lasts 40 minutes to 2 hours, and - where cooked pulp is concentrated at the bottom of the digester, and continuously, by equal rate as being feedstock fed into the digester, discharged from the bottom of the said digester by the conveyor having the hydraulic pressure compensation. (i) preparing the grass-like plant feedstock by comminuting to produce a feedstock with longitudinal size distributed from 1.5-30 cm and diameter of 0.5-15 mm, and with removed fine dusty particles by dedusting of said feedstock with fan; (ii) continuous digestion of a grass-like dust-free plant feedstock prepared in step (i) in a digester formed as a vertical column internally having only smooth side walls; where dust-free grass-like plant feedstock is continuously fed directly on the top of the said digester via conveyor; - in parallel with said dust-free feedstock top-feeding, the chemicals for digestion selected from the group consisting of NaOH and NaCl or Na 2 SO 3, fresh water, regenerated water, and steam are introduced continuously on the top of said digester; maintaining the digestion temperature from 70-100 °C and average composition of thus formed suspension during said continuous digestion within the following ranges: (a) 0.9-1.5% w/w of NaOH; (b) 0.15-0.4% w/w of NaCl or Na 2 SO 3; and (c) 15-18% w/w of grass-like plant feedstock; where concentrations of ingredients being calculated on the weight of the liquid phase; (a) 0.9-1.5% w/w of NaOH; (b) 0.15-0.4% w/w of NaCl or Na 2 SO 3; and (c) 15-18% w/w of grass-like plant feedstock; where concentrations of ingredients being calculated on the weight of the liquid phase; - where dissolution of noncellulosic substances from the grass-like plant feedstock is performed during the mass transfer from the top to the bottom of the said digester performed only by the gravity that lasts 40 minutes to 2 hours, and - where cooked pulp is concentrated at the bottom of the digester, and continuously, by equal rate as being feedstock fed into the digester, discharged from the bottom of the said digester by the conveyor having the hydraulic pressure compensation.