Abstract: Solving mechanical problems with Lagrangian is a very useful method. In this paper, the motion of free photons in the background of a black hole is solved by means of Lagrangian. After obtaining the four velocities of photons, the allowable motion range of photons with different energies is studied by means of the law of conservation of mechanical energy. Then, according to the inverse problem of kinematics in mechanics, the trajectory of photons is finally obtained.

Key words: Lagrangian, law of conservation of mechanical energy, black hole