In general, the majority of recent speaker recognition systems employ an i-Vector configuration as their front-end. Post-processing of i-Vectors usually requires a Linear Discriminant Analysis (LDA) phase to reduce the dimensions of the i-Vectors as well as improve discrimination of speaker classes based on the Fisher criterion. Given that channel, noise, and other types of mismatch are generally present in the data, it is better to discriminate the speaker’s data non-linearly. Generalized Discriminant Analysis (GDA) uses kernel functions to map the data into a high dimensional feature-space which leads to non-linear discriminant analysis. In this study, we replace LDA with GDA in an i-Vector based speaker recognition system and study the effectiveness of various kernel functions. It is shown, based on equal error rate (EER) and minimum of detection cost function, that GDA not only improves performance for regular test utterances, but is also useful for short duration test segments. NIST2010 Speaker Recognition Evaluation (SRE) core and extended-core (coreext) conditions are employed for experiments; in addition, we evaluate the system for short duration segments on the 10-sec test condition and truncated coreext test data. The relative improvement in EER is 20% for the cosine kernel employed here with GDA processing.