In this thesis, we give a brief review on the standard model in ordinary space. The characteristics of Noncommutative Space –Time and Standard Model in this space are discussed. In this framework, there are two approaches. In the first one, the symmetry group is U(3)×U(2)×U(1), which can be reduced to the standard model group via two spontaneou symmetry breaking. Besides the ordinary gauge Bosons, two new gauge bosons and two additional scalar particles appear in the NC- Space due to symmetry breaking. In the second approach, the group and the number of particles is similar to the group and the number of particles in the ordinary standard model. Meanwhile, the NC-fields through the Seiberg-Witten maps are determined as functions of the NC parameter. We consider the rare decays of the Z boson to Leptons- antileptons and photon in the NC-space. Consequently, we find a bound on the NC- parameter of the order of 20 GeV in such decay. We also consider the effect of Earth rotation on the amplitude and the decay rate of the Z-boson and we show that they depend on the time and location of the accelerator.