An equation of state (EOS) extended from statistical associating fluid theory (SAFT) has been proposed recently to describe the thermodynamic properties of non-polar fluids across the critical point (CP) (Fluid Phase Equilib. 186 (2001) 165). In this work, this EOS is modified further to describe the thermodynamic properties of polar fluids across the CP by taking into account the dipole-dipole interaction. The dipole-dipole term proposed by Twu and Gubbins (Chem. Eng. Sci. 33 (1978) 863, 879) is used in this work in which the effective dipole moment is approximated as a liner function of density (Ind. Eng. Chem. Res. 35 (1996) 4727). We call this series of EOS with improved results across the CP as SAFT-CP. The new EOS that contains the dipole-dipole term includes five parameters for each polar fluid: the segment number m, the segment non-spherical parameter alpha, the segment volume nu(00), the segment interaction parameter u(0)/k and adjustable parameter c for effective dipole moment. Twelve polar fluids including hydrogen sulfide, ammonia, chloromethane, 1,1-difluoroethane, 1,1,1-trifluoroethane, 1,1,1,2-tetrafluoroethane, diethyl ether, ethyl acetate, acetone, 2-butanone, 2-pentanone, and 2-heptanone are used as examples. Polar fluids with associating sites are not included in this work, such as water and alkanols. The SAFT-CP EOS reproduces the saturated pressure and liquid density date with an average absolute derivation (AAD) of about 1%. Critical temperatures, pressures and densities are calculated with the AAD less than 2%. In the one-phase region including supercritical region, the SAFT-CP represents the experimental values of density with an AAD of about 2%. The comparison of the calculated critical exponent P with the experimental one for ethyl ether shows the improvement in the region of temperature approximately up to (T-C - 2) K.