For a Fibonacci chain constructed recursively with S_m+1={S_m|S_m-1}, in a tight-binding model of single electron, we investigate numerically density of electronic states and electronic energy band structure with negative eigenvalue theory and three diagonally symmetric matrixes. Trifurcating structure of energy band of the system is demonstrated. With renormalization-group method and scattering theory, we study localization length and transmission coefficients of electronic states in a chain. At particular eigen-energies, extend states with localization lengths greater than size of the system are found and transmission coefficient is equal nearly to 1. At most eigen-energies, corresponding electronic states are localized states due to short localization length. In addition, relations between transmission coefficients and parameters of Fibonacci chain are qualitatively investigated.