The present invention relates to a process for producing cellulose with low inorganic impurities from sugarcane bagasse, the process comprising treating prehydrolysed sugarcane bagasse with a mixture of sulfite and at least one alkali to obtain residue having undissolved cellulose along with lignin rich liquor. The residue having undissolved cellulose is further subjected to delignification and addition of at least one enzyme to obtain a cellulose rich pulp. The cellulose rich pulp obtained is then treated with bleaching agents followed by separating pure cellulose rich pulp having high a-cellulose content and low inorganic impurities.