The three-nucleon system is reconsidered. The Faddeev equations are given leading to a set of integral equations. Solving these integral equations, suitable forms are considered for the nucleon-nucleon interaction. In the bound state of three-nucleon system, the form of the nuclear forces from the nucleon-nucleon interaction is important. In the present calculations, we consider the nuclear forces resulting from the nucleon-nucleon interaction by the exchange of a scalar meson, a pseudoscalar meson, and a massless vector meson. With this different meson exchange nucleon-nucleon interaction, the binding energy of the three-nucleon system is calculated by solving the Faddeev integral equations giving a value of 8.452 MeV.