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Nowadays, highly super charging is required corresponded to downsizing concept for improving thermal efficiency in direct-injected spark ignition (DISI) engine. However, highly super charging increases the possibility of super-knock caused by pre-ignition. Recently, in many studies, the reason of pre-ignition has been investigated but the reason why pre-ignition leads such strong knocking called super-knock has not been investigated. In DISI engine, it is estimated that there is more inhomogeneity of equivalence ratio and temperature of air-fuel mixture than it in port injection SI engine. In this study, factors which decide self-ignition timing was reviewed and the influence of inhomogeneity of air-fuel mixture to super-knock was investigated based on numerical calculation.