The notion of the thermodynamic entropy in the context of quantum mechanics is a controversial topic. Although there were proposals to refer von Neumann entropy as the thermodynamic entropy, it has its own limitations. The observational entropy has been developed as a generalization of Boltzmann entropy, and it is presently one of the most promising candidates to provide a clear and well-defined understanding of the thermodynamic entropy in quantum mechanics. In this paper, we study the behavior of the observational entropy in the context of localization-delocalization transition for one-dimensional Aubrey-Andr\'e (AA) model. We find that for the typical midspectrum states, in the delocalized phase the observation entropy grows rapidly with coarse-grain size and saturates to the maximal value, whereas in the localized phase the growth is logarithmic. Moreover, for a given coarse-graining, it increases logarithmically with system size in the delocalized phase, and obeys area law in the localized phase. We also find the increase in the observational entropy followed by the quantum quench is logarithmic in time in the delocalized phase as well as at the transition point, whereas in the localized phase it oscillates. Finally, we also venture the self-dual property of the AA model using momentum space coarse graining.