1. An internal combustion engine system equipped with an open-close timing variation mechanism constructed to vary an open-close timing of an intake valve for an internal combustion engine, the internal combustion engine system comprising: a learning instruction module configured to, upon satisfaction of an idle learning condition for learning a control amount required to idle the internal combustion engine as an idle control amount or upon satisfaction of an open-close timing learning condition for learning a control amount required to set an open-close timing of the intake valve to a specific open-close timing as an open-close timing control amount, give a learning instruction to perform learning of the idle control amount and learning of the open-close timing control amount; an idle learning module configured to learn the idle control amount, in response to the learning instruction given by the learning instruction module; and an open-close timing learning module configured to learn the open-close timing control amount, in response to the learning instruction given by the learning instruction module.