Entropy is an essential term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we estimate the Rényi entropy measure of a linear failure rate distribution when data are generalized type-II hybrid censored. The estimations with the maximum likelihood are obtained. With regard to the linex loss function, the Bayes estimates are suggested. The Bayes estimates for closed-form formulations are unavailable. The methods of significance sampling and Tierney and Kadane's approximation are thus used. To demonstrate the suggested approaches, two real datasets based on a generalized type-II hybrid censored scheme have also been analyzed for illustrative purposes. Simulation studies to evaluate the performance of the estimates with various sample sizes are described. Additionally, many criteria are suggested for contrasting various sample plans, such as relative mean squared error and relative bias for various censored samples. The Bayes estimators of entropy are superior to the maximum likelihood.