Surface cell Madelung constant is firstly defined in calculating surface free energy of nanosized crystal grains, which explains the physical performance of small crystals and may be great benefit to make surface analysis and study dynamics of crystal nucleus growth. A new ap- proximative expression of surface energy and relevant thermodynamic data was used in this cal- culation. A new formula and computing method for calculating the Madelung constant α of any complex crystals is proposed, and surface free energies and surface electrostatic energies of nano- sized crystal grains as well as Madelung constant of some complex crystals are theoretically cal- culated in this paper. The surface free energy of nanosized crystal grain TiO2 and surface elec- trostatic energy(absolute value) of nanosized crystal grain α-Al2O3 are found to be the biggest among other crystal grains.