I-vector based text-independent speaker verification (SV) systems often have poor performance with short utterances, as the biased phonetic distribution in a short utterance makes the extracted i-vector unreliable. This paper proposes an i-vector compensation method using a generative adversarial network (GAN), where its generator network is trained to generate a compensated i-vector from a short-utterance i-vector and its discriminator network is trained to determine whether an i-vector is generated by the generator or the one extracted from a long utterance. Additionally, we assign two other learning tasks to the GAN to stabilize its training and to make the generated i-vector more speaker-specific. Speaker verification experiments on the NIST SRE 2008 “10sec-10sec” condition show that after applying our method, the equal error rate reduced by 11.3% from the conventional i-vector and PLDA system.