Pb(111) film is a special system that exhibits strong quantum size effects in many electronic properties. The collective excitations, i.e., plasmons, in Pb(111) films are also expected to show signatures of the quantum size effect. Here, using high-resolution electron energy loss spectroscopy, we measured the plasmons on the surface of Pb(111) films with different film thicknesses and analyzed the plasmon dispersions. One surface plasmon branch exhibits prominent damping in the small momentum range, which can be attributed to the interaction between the top and bottom interfaces of the Pb(111) films. With the film thickness increasing, the critical momentum characterizing the damping in Pb(111) films decays not only much slower in Pb(111) films than in other metal films, and even in films with the thickness up to 40 monolayers the damping still exists. The slow decay of the surface plasmon damping, manifesting the strong quantum size effect in Pb(111) films, might be related to the strong nesting of the Fermi surface along the (111) direction.