The High Voltage CMOS (HV-CMOS) sensors are extensively investigated by the ATLAS collaboration in the High-Luminosity LHC (HL-LHC) upgrade of the Inner Tracker (ITk) detector. A testbeam telescope, based on the ATLAS IBL (Insertable B-Layer) silicon pixel modules, has been built to characterize the HV-CMOS sensor prototypes. The Front-End LInk eXchange (FELIX) system is a new approach to function as the gateway between front-ends and the commodity switched network in the different detectors of the ATLAS upgrade. A FELIX based readout system has been developed for the readout of the testbeam telescope, which includes a Telescope Readout FMC Card as interface between the IBL DC (double-chip) modules and a Xilinx ZC706 evaluation board. The test results show that the FELIX based telescope readout system is capable of sensor calibration and readout of a high-density pixel detector in test beam experiments in an effective way.