In order to solve the problem of the spectrum fragmentation in elastic optical networks, a fragmentation-aware routing and spectrum allocation algorithm for maximizing service carrying capacity is proposed in this paper. In the routing stage, K-shortest path routing algorithm is utilized to calculate K alternative paths with the minimum hops offline for connection requests. In the spectrum allocation stage, the factors such as the duration of the arriving request and established connections are considered to evaluate the service carrying capacity of the free spectrum block (SB). From available SBs of the selected path, we select the scheme that is beneficial to maximize the service carrying capacity of the free resource in the relevant paths after the lightpath is established for the connection establishment. Simulation results show that the algorithm can reduce the bandwidth blocking probability and the link average fragmentation ratio and improve the resource utilization.