This paper provides an entropy inference method based on an objective Bayesian approach for upper record values having the two-parameter logistic distribution. We derive the entropy based on i-th upper record value and the joint entropy based on the upper record values, and examine their properties. For objective Bayesian analysis, we provide objective priors such as the Jeffreys and reference priors for unknown parameters of the logistic distribution based on upper record values. Then, an entropy inference method based on the objective priors is developed. In real data analysis, we assess the quality of the proposed models under the objective priors.