Flexible resource has become very important in today's competitive environment. The improvements in manufacturing efficiency can be achieved by the use of optimal scheduling to max the potential power of flexible resource. In this paper, we formulate the Job Shop Flexible Resource Scheduling (JSFRS) problem in which the job operation processing times depend on the amount of resource assigned to an operation and review the main idea of Nested Partitions (NP) framework. Based on the model for JSFRS problem, we present a hybrid algorithm via Nested Partitions to solve it. In the hybrid algorithm, the JSFRS problem is considered as a partition tree. And use the generic partition strategy for effectively concentrating the sampling effort in those subsets of feasible regions. Genetic algorithm (GA) search and heuristic resource allocation strategy are incorporated into the sampling procedure, and we use the sample points to estimate the promising index of each region. Numerical examples are also presented to illustrate the hybrid approach.