Starch is a naturally occurring polymer with unique physicochemical properties and yet some key structural properties of starch that can be modified to meet specific requirements. The transition from starch to nano-starch and subsequent chemical modification provides a variety of benefits such as greater thermal stability and lower biodegradability. The preparation of potato starch nanoparticles (NPA) were prepared with combined methods of acid hydrolysis and sonication, after the NPA was made two modifications, a copolymer of potato starch nanoparticles grafted with polyacrylamide by free radicals, using persulfate of potassium (PSP), as initiator and carboxymethyl nano-starch of potato using potassium hydroxide as the activating agent and monochloroacetic acid as the esterifying agent, the two preparations were carried out by microwave irradiation. The true size of the nanoparticles could not be determined by SEM, because it presented agglomerations, the NPA obtained were amorphous, which indicated that the ultrasound affected the crystalline zones of the starch. The confirmation of the modification of the potato starch nanoparticles was observed by the presence of new bands in the infrared spectrum (FTIR), for the copolymer in 3191 and 1649 cm-1, the presence of the NH group and C = O respectively, and for the carboxymethyl nano-starch the presence of the carbonyl group at 1595 and 1406 cm-1. Finally, the grafted copolymer NPA-i-PAM (MCI-2) and carboxymethyl nano-starch potato (CMNPA), prepared above, were added and added to a water-based bentonite mud (8%), where an increase in viscosity was observed and decreased filtrate loss by 45 and 32% respectively, which indicated that these products could be used as additives in drilling muds as viscosifying and filtering reducing agents.