Short duration speaker verification is a challenging problem partly due to utterance duration mismatch. This paper proposes a novel method that modifies the standard Gaussian probabilistic linear discriminant analysis (G-PLDA) to use two separate generative models for i-vectors from long and short utterances which are jointly trained. The proposed twin model G-PLDA employs distinct models for i-vectors corresponding to different durations from the same speaker but shares the same latent variables. Unlike the standard G-PLDA, this twin model G-PLDA takes the differences between utterances of varying durations into account. Hyper-parameter estimation and scoring formulae for the twin model G-PLDA are presented. Experimental results obtained using NIST 2010 data show that the proposed technique leads to relative improvements of 8.5% and 15.6% when tested on utterances of 5 second and 3 second durations respectively.