We developed a many-body method to calculate the electron correlated basis function of excited state. Based on the Chakravarty-Woo equation and functional expansion and convolution approximation, we got the linear integral iteration equation for the variation of density and correlation function, so the wave function, due to electron excitation. A general formula for excitation energy in many-body problem is obtained From this and the known experimental data, we found the energy gap and electron correlation in 1-d conducting polymer. The result is in good accordance with the experiment.