To meet the differentiated requirements of computing offloading traffic and traditional broadband traffic in multi-access edge computing(MEC) empowered fiber-wireless access networks, this paper proposes a cooperative offloading-aware(COA) dynamic wavelength and bandwidth allocation (DWBA) algorithm based on hybrid scheduling and cooperative offloading mechanism. The algorithm returns computing results by online scheduling, and divides the offline sub-cycle into the computing offloading sub-cycle and broadband traffic sub-cycle. The optical line terminal collaboratively schedules wavelength and bandwidth allocations and offloading decisions, and selects the offloading target for the overloaded MEC server by horizontal computing cooperative offloaing scheme preferentially, and then it offloads the remaining computing requirements to the remote centralized cloud. The simulation results show that the algorithm can improve the completion rate and reduce the completion time of computing tasks, and reduce the adverse impact on traditional broadband traffic and core network load.