New 6-parameters extended form of the Kobayashi's generalized gamma function is defined, several of its properties and recurrence formulas are derived. Based on this new function we introduce a new 6-parameters with a model function extended generalized gamma distribution. Many new distributions are shown to be particular cases of this suggested distribution, including some familiar known distributions. In terms of the model function statistical properties; reliability and hazard functions, and estimation of some parameters of the distribution are studied. Also, the form of the distribution is considered under various forms of the model function. We believe that this new distribution model is reasonable for accommodate multi various applications, since it have wide variety of shapes. Especially, for the life distribution of a component where the presence of the displacement and intensity parameters is vitally important.