The constant increase in energy demand necessitates exploration of new oil fields at challenging reservoir environments. A proper selection of the drilling fluid, or a drilling mud, is crucial in minimizing the cost and time required for the drilling process. The circulating drilling fluid aids in cooling, lubricating the drilling bit and in removing the rock cuttings from the drilling well. Water-based muds are widely used as a drilling fluid in oil and gas industry while exploring the hydrocarbon. During deep-sea drilling activities at extreme depths, high-temperature and high-pressure (HTHP) conditions are encountered. These results in overheating of drilling equipment and malfunction due to lost circulation posing a severe limitation to the drilling fluid used. Several studies have been conducted to enhance the rheological and thermal properties of water-based drilling muds. Owing to the enhanced thermo-physical properties and stable nature, suspensions of nanoparticles have been suggested to be used along with drilling fluids for such conditions. Colloidal suspensions containing nano-sized particles (1-100nm) in a basefluid are generally termed nanofluids. Rheological characteristics of various nanofluids prepared from different types of nanoparticles have been thoroughly studied in the past. However, the effect of nanoparticles on drilling fluids at high temperature and pressure conditions are not investigated in detail. In the present work, the rheological study of nanomud suspensions prepared by adding multi-walled carbon nanotubes (MWCNT) into the drilling fluid is conducted. A Nanofluid suspension based on CNT is deemed advantageous due to its high thermal conductivity, and efficient mechanical properties. High-pressure and high-temperature rheology of a nanomud suspension is reported here. The CNT-drilling mud nanofluids (nanomuds) are prepared using a top-down approach. Initially, the water-based drilling mud (base fluid/basemud) is prepared. The Water Based Mud (WBM) used in this study contain Bentonite (1%) and Barite (7%) which makes up the total percentage of solids by volume of the whole mud with a 12.5ppg (pounds per gallon) as the final weight. The Bentonite was initially mixed with the water and seated for approximately 16 hours of hydration to form Prehydrated Bentonite or PHB. A high-pressure high-temperature (HPHT) viscometer (Chandler Viscometer 7600) is used for the rheological analysis. The viscometer is designed for rheological studies of drilling fluids while subjected to varying drilling well conditions in accordance with ISO 10414-1, 10414-2 and API 13 recommended practices. As the variation of the pressure and temperature would influence the measured viscosity values of the suspension, two independent experimental schedules are performed. Automated measurements are recorded once the pressure and temperature values of the sample have reached the set values. Viscosity values are measured at a maximum pressure of 170MPa with temperatures ranging from ambient to 180C. The effect of MWCNT nanoparticle concentration and variation in shear rate are also investigated. A shear thinning non-Newtonian behavior is observed for the basemud and the nanomud samples at all pressures and temperatures. The basemud showed an increase in viscosity with an increase in pressure. However, with MWCNT particle addition, this trend is observed to have reversed.