We want to explore matter which is formed the Universe in earlier time. We have had lots of success in particle physics frontier within the standard model (SM). However, some phenomena in the nature that SM cannot explain yet, so that we need to extend the SM gauge group as a new gauge boson Z' of U(1) gauge symmetry with charged lepton number Li; i can be electron, muon, or tau. Next, we apply the observation of supernova 1987A (SN1987A) in the determination of Z' decay length and luminosity. In this thesis, we try to figure out the new model with constrains on it mainly; specifically, constraints on two additional parameters which are gauge coupling constant, gZ' and mass of new gauge boson Z', mZ'. Therefore, we will estimate a specific range of gZ' and mZ' (MeV) in considering constraints on new light gauge boson Z' from the observation SN1987A.