In this paper, we investigate the problem of entropy estimation for the inverse exponential Rayleigh distribution under progressively Type-Ⅱ censored samples. For the Shannon entropy of the inverse Rayleigh distribution, the maximum likelihood estimation and Bayesian estimation are studied, as well as the interval estimation. Under the Bayesian method, we used three different loss functions to discuss the Shannon entropy under each of these loss functions. The three loss functions are as follows: the weighted squared error loss function, the K-loss function, and the precautionary loss function. The Bayesian estimates of Shannon's entropy under these three loss functions are computed using the Lindley approximation and mixed Gibbs sampling. Finally, we calculated the estimated values, mean squared errors, and variances of the estimators through Monte Carlo simulations. To evaluate the performance of the estimation methods, we chose to use the mean squared errors for a comparative analysis. In the subsequent step, we applied the estimated results to a real dataset.