In this work, a Bayesian approach to speaker normalization is proposed to compensate for the degradation in performance of a speaker independent speech recognition system. The speaker normalization method proposed herein uses the technique of vocal tract length normalization (VTLN). The VTLN parameters are estimated using a novel Bayesian approach which utilizes the Gibbs sampler, a special type of Markov Chain Monte Carlo method. Additionally the hyperparameters are estimated using maximum likelihood approach. This model is used assuming that human vocal tract can be modeled as a tube of uniform cross section. It captures the variation in length of the vocal tract of different speakers more effectively, than the linear model used in literature. The work has also investigated different methods like minimization of Mean Square Error (MSE) and Mean Absolute Error (MAE) for the estimation of VTLN parameters. Both single pass and two pass approaches are then used to build a VTLN based speech recognizer. Experimental results on recognition of vowels and Hindi phrases from a medium vocabulary indicate that the Bayesian method improves the performance by a considerable margin.