We propose a new low-diameter interconnection network called FleX, which offers high f lexibility when installing interconnections in a HPC system. FleX consists of multiple layers with only connections between neighboring layers and not within each layer. These structural properties make it easy to achieve a low diameter with regardless of the scale. The cross-like connections between the adjacent layers in FleX impart various alternative minimal paths, allowing FleX to have high resiliency and a wide bisection width. We also discuss the minimal routing scheme and a stochastic load balancing scheme (LBR) for the proposed interconnection network. Through cycle-based simulations, the performance of FleX is evaluated, and the cost and power consumption analyses in comparison with other interconnection networks are also conducted. We verify that FleX has high configuration flexibility with regard to cost and performance, and also provides low latency and high saturation throughput with the same cost over the legacy interconnection networks for the HPC system. Moreover, being synergied with the proposing LBR, we also verify that FleX can expand its saturation throughput further while only sacrificing the latency slightly.