The accurate terrain classification in real time is of great importance to an autonomous robot working in field, because the robot could avoid non-geometric hazards, adjust control scheme, or improve localization accuracy, with the aid of terrain classification. In this paper, we investigate the vibration-based terrain classification (VTC) in a dynamic environment, and propose a novel learning framework, named DyVTC, which tackles online-collected unlabeled data with concept drift. In the DyVTC framework, the exterior disagreement (ex-disagreement) and interior disagreement (in-disagreement) are proposed novely based on the feature diversity and intrinsic temporal correlation, respectively. Such a disagreement mechanism is utilized to design a pseudo-labeling algorithm, which shows its compelling advantages in extracting key samples and labeling; and consequently, the classification accuracy could be retrieved by incremental learning in a changing environment. Since two sets of features are extracted from frequency and time domain to generate disagreements, we also name the proposed method feature-temporal disagreement adaptation (FTDA). The real-world experiment shows that the proposed DyVTC could reach an accuracy of 89.5%, but the traditional time- and frequency-domain terrain classification methods could only reach 48.8% and 71.5%, respectively, in a dynamic environment.