A Monte Carlo arithmetic method is utilized to investigate the Peierls transition in the linear and circular carbon nanowire respectively. The carbon nanowires interacting with the 6 nearest neighbors in hexagonal structure are spaced by 0.3 nm. Despite the Peierls transition of the linear carbon nanowires is unaffected by the Van der Waal’s force, we discovered that the Peierls transition temperature of the isolated curved nanowire is raised to 910K under curvature. Based on the simulation results, the fluctuation of the atomic position of the atoms are stronger near to the free end boundary condition. Applying stress on the interstitial doped carbon nanowire array examines the elastic modulus which shows above 6TPa. The geometrical effect on the electronic density of states of the kink structural carbon chain is simulated by Harris functional in combination with Local Density Approximation. Two different lengths of branches A and B, are occupied alternatively to generate the asymmetric carbon chain. The ratio of the asymmetric branch length, RAB = A / B, plays an important role in the electronic density of states DOS around Fermi level . The highest DOS(EF) occurs if the RAB equals to 2 and while the Fermi level coincides with the Von-Hove singularity at RAB = 3.