The widely adopted i-vector performances well in text-independent speaker verification with long speech duration. How to integrate the state-of-the-art i-vector framework into the text-prompted speaker verification is addressed in this paper. To take advantage of the lexical information and enhance the performance for speaker verification with random digit sequences, this paper proposes to extract a set of digit-dependent local i-vectors from the utterance instead of extracting a single i-vector. The digit-dependent local i-vector is considered
to represent speaker-digit combination information, not just speaker vocal tract information. Experiments on Part III of the RSR2015 dataset show that the digit-dependent local i-vector is superior to DNN i-vector and phone-dependent local i-vector for text-prompted speaker verification task.