Rayleigh-Benard convection is one of the typical natural convection that appears in a fluid layer with heated bottom and cooled top planes. Although the velocity field of the convection may be steady when the temperature difference is small, it may start to oscillate slightly by even oscillatory instability when the temperature difference is increased. It is known that some fluid particles may be transported chaotically in the Lagrangian description in such flow, even when the velocity field seems to be stable in the Eulerian description. In this study, we have experimentally detected the Lagrangian coherent structures (LCSs), which are invariant manifolds in non-autonomous systems, in perturbed Rayleigh-Benard convection from two-dimensional velocity data obtained by Particle Image Velocimetry (PIV) and have clarified the global structures of fluid transport. We have found that repelling and attracting LCSs entangle with each other in the vicinity of cell boundaries and create some lobes in which fluid particles are transported to another lobe in each period of the perturbation. We have also found that a figure-eight LCS appears in the middle of each cell.