Abstarct: From the begining of the history of nuclear physics to now, using a model that is be able to provide a good descxription of the nucleons behavior which is affected by the nuclear force between them, has been in high importance. The hyperspherical harmonics expansion method is one of the safest and most successful methods to study the many-particles systems in the relativistic and nonrelativistic quantum mechanics. We want to find the correct form of the Schrödinger equation for Triton three-nucleon nuclear system by this method and then solve it in order to theoretical study of ground state and probability of existence of excited bound state. For this purpose, using a potential that provide a good estimation of ground state static propertice (energy and rms charge radius) is very important in reaching a phenomenological model. First, we have used the Yukawa potential as nuclear potential in Triton and in the next step for get closer to the experimental values and real potential, we have added a correction term. in both cases the results have been presented and compared whit experiment. We have used from the shooting numerical method for solving the Schrödinger equation. it’s a suitable selection for exact solving of this equation specially in the presence of those of potentials that there is not exact solution for them (for example Yukawa potential). The shooting method is baxsed on another numerical algorithm such as Newton-Rafson root-finding and Runge-Kutta methods.