In space-division multiplexing elastic optical networks(SDM-EON) based on multicore fiber(MCF), one of the problems is the physical impairment of transmission signals due to inter-core crosstalk. From the perspective of spectrum allocation and core selection, this paper proposes a crosstalk-aware spectrum allocation algorithm for SDM-EON. In this algorithm, when allocating spectrum resources for service requests, crosstalk within a single request and between requests can be minimized by avoiding filling adjacent cores. The numerical simulation results show that the algorithm can effectively improve the crosstalk problem while maintaining a low bandwidth blocking probability in NSFNet and USNet network topologies.