A 45 GHz superconducting ECR ion source FECR (a Fourth generation Electron Cyclotron Resonance) is under construction at IMP. A total current of more than 20 emA is expected to be extracted from the source. Therefore, the extraction voltage is designed to be biased up to 50 kV to reduce the effect of space charge. An on-line movable four-electrode system will be adopted so that the plasma meniscus and initial beam formation can be optimized by adjusting the distance between the plasma electrode and puller. After being extracted, the multi-species ion beam will be focused by two solenoids and then analyzed by a 110-degree dipole. A sextupole magnet is planned to be placed after the dipole to reduce the non-linearities of the beam induced by the sextupole field of the ion source. This paper will present a design of the beam extraction and transport system for this new ion source. The advantage of the dual-solenoid scheme and the effectiveness of the non-linearity correction both by simulations and experiments will also be discussed.