A new routing algorithm for MPLS (Multi-Protocol Label Switching, MPLS) traffic engineering in SDN-based (Software Defined Network, SDN) satellite switching networks is presented in this paper. LSP (Label Switched Path, LSP) link initial weights are defined as composite functions consisting of link transmission delay, residual bandwidth and BER (Bit Error Rate, BER). Based upon ISL (Inter-Satellite Link, ISL) handoff, LSP link stability function is defined. Next, LSP link criticality function is defined by the frequency of ISL used to establish LSP. The LSP link selection probability function is designed based on the three functions mentioned above. The proposed routing algorithm is able to implement dynamic routing from the source to the destination of multiple LSPs, which can balance the load of network traffic. Some numerical simulations are made to test the validity and capability of the proposed routing algorithm.