The Plerion nebula is characterized by its pulsar that fills the center of the supernova remnant with radio and X-ray frequencies. In our galaxy there are nine naked plerionic systems known, of which the Crab Nebula is the best-known example. It has been studied this instance in order to investigate how the pulsar energy affect on the distribution and evolution of the remnant as well as study the pulsar kick velocity and its influence on the remnant. From the obtained results it's found that, the pulsar of the Crab Nebula injects about (2−3)𝑥 1047 erg of energy to the remnant, although this energy is small compared to the supernova explosion energy which is about 1051 erg but still plays a significant role in the distribution and the morphology as well as the dynamical expansion of the remnant. However, most of this energy is concentrate in the direction of the pulsar rotational dipole axis which makes the remnant expanding in this direction further than other regions and consequently has more density. Moreover, it's found that the pulsar kick velocity which is in order ≈110 km.s-1 also adds an expansion energy to the remnant in the direction of the kick (North West direction) added to its initial energy and due to this kick the pulsar will be shifts to the opposite direction of the kick the South East direction, which cause the pulsar to leave its birth position and finally leave the remnant itself.