Network slicing enables diversified services to be accommodated by isolated slices in network function virtualization-enabled software-defined networks. To maintain satisfactory user experience and high profit for service providers in a dynamic environment, a slice may need to be reconfigured according to the varying traffic demand and resource availability. However, frequent reconfigurations incur certain cost and might cause service interruption. In this paper, we propose a hybrid slice reconfiguration (HSR) framework, where a fast slice reconfiguration (FSR) scheme reconfigures flows for individual slices at the time scale of flow arrival/departure, while a dimensioning slices with reconfiguration (DSR) scheme is occasionally performed to adjust allocated resources according to the time-varying traffic demand. In order to optimize the slice’s profit, i.e., the total utility minus the resource consumption and reconfiguration cost, we formulate the problems for FSR and DSR, which are difficult to solve due to the discontinuity and non-convexity of the reconfiguration cost function. Hence, we approximate the reconfiguration cost function with ${L} _{1}$ norm, which preserves the sparsity of the solution, thus facilitating restricting reconfigurations. Besides, we design an algorithm to schedule FSR and DSR, so that DSR is timely triggered according to the traffic dynamics and resource availability to improve the profit of slice. Furthermore, we extend HSR with a resource reservation mechanism, which reserves partial resources for near future traffic to reduce potential reconfigurations. Numerical results validate that our reconfiguration framework is effective in reducing reconfiguration overhead and achieving high profit for slices.