A graft copolymer is synthesized with graft copolymerization of acrylamide (AM) and 1‐vinyl‐2‐pyrrolidone (NVP) grafting onto sodium carboxymethyl starch (CMS) via central composite design (CCD). The initiation system consists of potassium persulfate (KPS) and sodium hydrogen sulfite (SBS). The copolymer is confirmed by infrared spectroscopy, nuclear magnetic resonance hydrogen spectroscopy, scanning electron microscopy, thermogravimetric experiment, and elemental analysis. The rheological performance, filtration loss, cake thickness, and cake fictional coefficient of the drilling mud containing copolymer are evaluated. The results show that copolymers have ability to thicken and reduce filtration volume and have no obvious influence on the thickness and fictional coefficient of the mud cake. Response surface methodology (RSM) is exerted for variable evaluation and optimization. The results indicate that initiator concentration is the main contributing factor to decrease filtration volume and the optimum results are 1.5 wt% (initiator concentration), 1.82 (mole ratio of monomer to starch [AGU]), 66.02 °C (reaction temperature), 3.87 h (reaction time). The predicted value and the actual experimental value are 8.64 and 9 mL respectively with an error of 4.01%. The small error indicates that there is a small deviation between the actual and the predicted values, which also shows that the model is reasonable.