The molecular dynamics trajectory of a protein molecule is frequently characterized by the strongly anharmonic dynamics on the rugged potential surface. We herein propose a model, moving normal mode coordinates, to describe the anharmonic protein motions recorded in the trajectory, particularly those occurring in the low-frequency or large-amplitude normal mode space. A set of normal mode coordinates is defined at each time instant of the trajectory by principal component analysis (PCA) with a small time window. The time evolution of the normal mode coordinates defines the moving normal mode coordinates, the axes of which are translated and rotated time-dependently along the trajectory. Because the harmonic part of the dynamics is accounted for by the PCA in a quasi-harmonic manner, the motions of the coordinate system are expected to represent the anharmonic part of the protein dynamics. We applied this model to the analyses of molecular dynamics trajectories of a small protein, myoglobin. Translation of the origin of the coordinates was decomposed into diffusion and motions confined in a concave potential well. Significant parts of both types of motions occur in the large-amplitude normal mode space. Rotation of the large-amplitude normal mode space was characterized by fast relaxation completed within the time window of PCA but was confined through the entire trajectory in a small space spanned by a limited number of large-amplitude normal modes. The influences of temperature and the solvation condition are also discussed.