Numerical simulation of $CO_2$ addition effects to fuel and oxidizer streams on flame structure has been conducted with detailed chemistry in H$_2$-O$_2$ diffusion flames of a counterflow configuration. An artificial species, which displaces added $CO_2$ in the fuel- and oxidizer-sides and has the same thermochemical, transport, and radiation properties to that of added $CO_2$, is introduced to extract pure chemical effects in flame structure. Chemical effects due to thermal dissociation of added $CO_2$ causes the reduction flame temperature in addition to some thermal effects. The reason why flame temperature due to chemical effects is larger in cases of $CO_2$ addition to oxidizer stream is well explained though a defined characteristic strain rate. The produced CO is responsible for the reaction, $CO_2$＋H=CO＋OH and takes its origin from chemical effects due to thermal dissociation. It is also found that the behavior of produced CO mole fraction is closely related to added $CO_2$ mole fraction, maximum H mole fraction and its position, and maximum flame temperature and its position.