Neutrino is one of the nuclear particles that are necessary for the correct description of nuclear beta decay. The standard idea is that it is a massless neutral particle and its existence was postulated in order to save the conservation of ener gy principle. This particle was later detected experimentally and it is now known that neutrino has mass. The problem of astrophysical neutrino detection has produced a new phenomenon of neutrino oscillation where the three neutrino flav ours can oscillate between themselves. This paper studies the two component neutrino oscillation problem. We study the neutrino oscillation by using the Lagrangian formulation. In our study, we assume that the neutrinos are produced as n eutrino mass eigenstate and propagate in the vacuum in the superposition of two neutrino flavour state. The Lagrangian for neutrinos with their mass and the oscillation terms were obtained. By using the mass matrix in the Lagrangian, we formulate the time evolution operator in the interaction picture. The neutrino oscillation probability obtained by using the Lagrangian formulation have the same result with the one obtained by using quantum mechanics formulation. This study hopes to gain some deeper understanding into the behaviour of neutrino beyond the Standard Model.