In this paper, a novel approach is presented for text-independent speaker verification. A quantized acoustic trajectory is constructed for each utterance based on Universal Background Model (UBM). Analysis of the speaker entropy in the trajectory space demonstrates that the segmental trajectory catches some speaker-specific information, which can be used to discriminate different speakers. Gaussian component strings are proposed to reflect the dynamic features in the segmental trajectory. Based on the occurring frequencies of different component strings in the non-target and target speaker data, a Universal Background Trajectory Model (UBTM) and multiple Target Trajectory Models (TTMs) are created for background and target speakers separately. The experiments are conducted on the telephony speech used in the NIST 1999 speaker verification evaluation. The experimental results show that the bi-component strings achieve better performance compared to the uni-component and tri-component strings. The trajectory models can be combined with a general speaker verification system to provide complementary information.