The study on mitochondrial genome is one hot field in recent molecular biology. The progress of mtDNA research now concentrate on the expression, control and heteroplasmy of mtDNA, and the relationship between the mitochondrial genome and the nuclear genome. However, the discovery in the paternal inheritance of mtDNA brings new sight on traditional inheritance of mtDNA. With the widely using of mtDNA as a genetic marker in population and evolutionary biology, the neutral evolution of mtDNA with respect to fitness and the nuclear DNA has been challenged by nonneutral evolution behavior of mtDNA.