Resource　allocation　in　mobile　edge　computing　(MEC)-based　wireless　networks　with　energy　harvesting　has　attracted　great　attention.　However,　existing　works　assume　that　mobile　devices　are　stationary　while　harvesting　energy.　In　this　paper,　an　uplink　resource　allocation　strategy　is　developed　in　MEC-based　heterogeneous　networks.　A　random　mobility　model　is　designed　to　describe　the　movement　of　the　user　equipment　(UE).　Meanwhile,　the　UE　can　harvest　energy　from　six　frequency　bands　while　moving　along　a　certain　path.　The　energy　harvesting　model　of　the　UE　is　given　by　an　integral　expression.　The　objective　of　the　resource　allocation　problem　is　to　maximize　the　energy　efficiency　(EE)　under　the　constraints　of　energy　consumption,　total　data　rate　requirement,　sub-carrier　allocation,　and　transmission　power.　A　quantum-behaved　particle　swarm　optimization　(QPSO)　algorithm　is　employed　to　obtain　a　sub-optimal　solution.　Numerical　results　show　that　the　amount　of　energy　harvested　by　the　UE　decreases　as　the　moving　speed　increases.　Moreover,　the　QPSO　algorithm　has　higher　EE　than　an　existing　particle　swarm　optimization　algorithm.