For the Fibonacci sequence constructed by following the inflation rule A→AB and B→A, using the one-dimensional random walk model and Hurst’ analysis, we calculate numerically the auto-correlation function, the pseudo standard deviation of displacement defined by ourselves and the rescaled range function and investigate systematically the statistical properties. The results are compared with that of one-dimensional random binary sequence. We show that the Fibonacci sequence presents correlated behavior as well as scaling invariability and self-similarity. In addition, basing on the tight-binding model of the single electron and transfer matrix method, we study the charge transfer properties of Fibonacci sequence and discuss specially the dependence of electron transmission on energy and the length of the sequence. We find some resonant peaks can survive in relatively longer Fibonacci sequences than in random sequences, which also implies that there are long-range correlations in Fibonacci sequences.