The geometry and the electronic structure of the tetracyclo[6. 2.2.1(3,6).0(2,7)]trideca-4,9,11-triene-9,10-dicarboxylic anhydride (TTDA) have been investigated by DFT/B3LYP and /B3PW91 methods using the 6-311G(d,p) and 6-31+G(d,p) basis sets. Anhydride double bond of TTDA molecule is anti-pyramidalized. Potential energy surface of addition reaction of 1,3-cyclohexdiene to TTDA molecule (syn,endo-, syn,exo-, anti,endo- and anti,exo- addition) is calculated by B3LYP/6-31+G(d,p) method and configurations (transition states and products) corresponding to stationary points (saddle points and minima) is determined. Kinetic and thermodynamic parameters of cycloaddition reactions have also been calculated. Syn addition reactions have lower activation energies, enthalpies, entropies and free energies than anti addition reactions. According to the results of theoretical calculations, syn addition reactions are expected to occur. The most stable reaction product is of the syn,endo-addition reaction. There is a correlation between the syn-pi-face selectivity of the cycloaddition reaction and the pyramidalization of anhydride double bond of the TTDA molecule.