To address the path selection for quantum communication between any two users around the world， according to the structural characteristics of the dandelion spherical quantum satellite network， a quantum routing scheme with two-end entanglement exchange is proposed. In this scheme， entanglement is established from the source node and the destination node to the intermediate node， and the Bell measurement results are transmitted through the wireless channel， so as to complete the transmission process of quantum state information from the source node to the destination node. Simulation results show that： with the increase of the number of switching satellites， the two-end entanglement exchange routing scheme can effectively reduce the transmission time of quantum information； with the increase of the number of switching satellite nodes， the quantum channel establishment rate of the two-end entanglement exchange routing scheme is significantly superior to that of the hop by hop entanglement exchange scheme， and its routing transmission cost is less than that of the hop by hop entanglement exchange scheme. It can be seen that the quantum routing scheme of the two-end entanglement exchange has the advantages of short information transmission time， high quantum channel establishment rate， and small wireless transmission overhead.