Abstract: This research work discusses on the estimation of an unknown rate parameter of an Exponential distribution using Bayesian methodology under the Al-Bayyati’s loss function with different prior distributions. The rate parameter of an Exponential distribution is assumed to follow non-informative prior distribution (such as extension of Jeffrey’s prior distribution) and informative prior distribution (such as Gamma prior distribution, Gamma-Chi-square prior distribution, Gamma – Exponential prior distribution and Chi-square-Exponential prior distribution).