So far, many researchers have studied the bound three and four-nucleon systems, and using two and three-nucleon forces, they have applied the different methods to calculate the binding energy of such systems. Determining the stability or, in fact, the binding energy of single lambda-proton hyperon (?-p) is the main goal of the current research. Most of the Hyperon-Nucleon interactions (Y-N) are the One-Boson Exchange interaction (OBE), which is obtained using the YN and NN data in the same direction. In this project, the potential of ? and proton is very important, and for this two-body system we applied the expansion of Gaussian basis. First, we considered the Gaussian potential domains as our initial computing data (and because the potentials are complex, they are assumed to have real and imaginary parts). Then, using Schr?dinger equation and performing the corresponding calculations, we obtained the binding energy of the particles. And at the end of the calculations, the real part of the energy is the main answer and the imaginary part is the width. Also, by repeating the calculations, we can change the number of Gaussian basis to achieve the optimal answer; Here, the number of Gaussian basis N =30 is the optimal answer for the correct binding energy correspond to the binding energy of other researches. Finally, using these methods and comparing the results of the efforts made in this field, we evaluated the values obtained for the binding energy of ? and p. For example, for the potential amplitude -3770MeV with a Range=0.3 fm, the binding energy obtained -59.165MeV and for - 1160MeV with a Range=0.2 fm, the binding energy is equal to -50.39MeV, which corresponds to the values reported in previous works[51].