The present invention involves the use of a novel membrane system for natural gas upgrading. This membrane system includes a first-stage membrane such as a membrane prepared from the polymer of intrinsic microporosity (PIM) to selectively remove hydrocarbons from C3 to C35 to control the dew point of natural gas, and a second-stage membrane such as a polybenzoxazole (PBO) or crosslinked PBO membrane to selectively remove CO2 from natural gas. The new membrane system described in the current invention eliminates the use of high cost and high footprint membrane pretreatment. Therefore, the membrane system can significantly reduce the footprint and cost for natural gas upgrading compared to the current commercially available membrane systems that include a non-membrane-related pretreatment system.