A continuous process for production of cellulose pulp from grass-like plant feedstock for paper making. The process includes: preparing the grass-like plant feedstock by comminuting, dedusting, continuous digestion, disperging, diluting the cellulose pulp, screening and fractionation, concentration to remove black liquor, dilution with fresh water, and, optionally, pulp bleaching processes. The continuous digestion is performed in the vertical column at 70-100° C. for 40 minutes to 2 hours; average composition of thus formed digestion suspension is maintained within the following ranges: 0.9-1.5% w/w of NaOH; 0.15-0.4% w/w of NaCl or Na2SO3; and 15-18% w/w of grass-like plant feedstock; concentrations of ingredients being calculated on the weight of the liquid phase. Screening and fractionation are resulting with two fractions; one being further processed by milling, and another being further processed to final pulp with or without bleaching processes. The preferred grass-like feedstock for the process is miscanthus/Miscanthus×giganteus, Andersson/.