We derive an Ellipsoidal StatisticalBGKmodel for a polyatomic gas that is based on a general framework introduced in [1]. The distribution function of polyatomic gas depends on its velocity and a general internal energy function, that can be discrete or continuous. We solve the minimization problem of Boltzmann entropy under suitable moments and we determine the transport coefficients (Prandtl number, first and second viscosity) in the hydrodynamic limit. The model covers in particular the non polytropic case. [1] Borsoni, T., Bisi, M., Groppi, M. (2022). A general framework for the kinetic modelling of polyatomic gases. Communications in Mathematical Physics, 393(1), 215-266.