We consider the one-dimensional totally asymmetric asymmetric simple exclusion process. We particularly concentrate on the case where each hopping rate depends on each particle. In the step initial condition, where all sites from the left of some site are occupied and all other sites are empty, we discuss a dynamics of a particular particle (tagged particle). We show that the position fluctuation of the tagged particle is equivalent to the largest eigenvalue fluctuation of the Gaussian Unitary Ensemble (GUE) in the random matrix theory.