We examine vibronic coupling in the first five electronic states ((X) over tilde (2)Pi(g)-(A) over tilde (2)Pi(u)-(B) over tilde (2)Sigma(+)(g)-(C) over tilde (2) Sigma(+)(u)-(D) over tilde (2)Pi(g)-(E) over tilde (2) Pi(u)) of dicyanodiacetylene radical cation (C6N2 center dot+) in this article. Prompted by the prediction of its existence in the astrophysical environment, the vibronic band structure of these electronic states of C6N2 center dot+ has been probed in spectroscopic measurements in laboratory by various groups. Inspired by numerous experimental data, we undertook the task of investigating topographical details of electronic potential energy surfaces, their coupling mechanism and nuclear dynamics on them. The degenerate Pi electronic states of this radical are prone to Renner-Teller instability, and in addition symmetry allowed Sigma-Pi and Pi-Pi vibronic coupling is expected to play crucial role in the detailed vibronic structure of each of the above electronic states. A vibronic coupling model is developed here and first-principles nuclear dynamics study is carried out employing quantum mechanical methods. The vibronic band structure thus calculated is compared with experimental results and the progressions are identified and assigned. The nonradiative internal conversion dynamics among electronic states is also examined and discussed in relation to the various coupling of electronic states.