Classical flexible job-shop scheduling problem (FJSP) does not consider the transportation time of jobs movement among different machines, which reduces the potential significance of its practical applications. This paper defines an FJSP problem with transportation time incurred by movement of jobs with one Automated Guided Vehicle (AGV) and one Load/Unload (L/U) station. A filtered beam search (FBS) based meta-heuristic algorithm is presented to solve this problem. The detailed procedure of the algorithm is described, and an example is shown to illustrate the algorithm. Finally, preliminary experimental results with comparisons of other dispatching rules demonstrate the feasibility and effectiveness of the proposed algorithm for the FJSP with transportation time.