1. Abstract As exploring for oil and gas traps becomes more extreme in term of depths, the companies start to search for modern technologies and equipment for drilling under HPHT conditions. One of the challenges of HPHT deep water well is narrow margin between the fracture pressure gradient and pore pressure gradient, therefore prediction and control of well hydraulics is indeed vital. The solution for the HPHT deep water challenges is a technology of Managed Pressure Drilling (MPD). Riser less drilling is one of the types of MPD. It uses two different annular pressure gradients for maintaining required bottom hole pressure to drill a well This study presents a new approach for accurate determination and optimization of well hydraulics for MPD (Riser less drilling) under HPHT conditions. This approach depends on accurate prediction and determination of borehole temperature, mud density and pressure, mud rheology and hydraulics profiles inside wellbore under HPHT conditions. This work shows the comparison between well hydraulics that calculated by constant fluid properties (i.e independent on pressure and temperature conditions) and well hydraulics that calculated by taking into account the effect of pressure and temperature on fluid properties. This paper also shows the effect of drill pipe tool-joint, drilled cutting, annular eccentricity and drill string rotation pressure losses on well hydraulics for MPD. The objectives were achieved by designing computer simulator called ‘’HPHT MAT’’. A case study by using ‘’HPHT MAT’’ simulator to show the correct procedure for optimization the well hydraulics of MPD is introduced. The results show that accurate prediction and determination of temperature and mud rheology modelling is highly required for accurate planning and designing of MPD hydraulics. The pressure difference between the drill pipe and annulus in Riser less drilling must be taken into consideration during the calculation of the density, plastic viscosity, yield point and ECD profiles inside wellbore. Neglecting the effect of pressure and temperature on mud properties in the well hydraulics calculation will lead to erroneous results which may lead to a kick or a loss of circulation. Pressure losses due to drill pipe tool-joint, drilled cutting, annular eccentricity and drill string rotation have significant effect on well hydraulics of MPD. New technique for calculating the well hydraulics of MPD by using finite difference calculation is developed. 2. Keywords: <span style=font-size: 10.0pt;font-family: times= new= roman,serif=>Dual Gradient Drilling; High Pressure and High Temperature Condition; Managed Pressure Drilling; Riser Less Drilling