In the current study, three 6FDA1/BPDA1-based polyimides (PIs) containing different diamine moieties (DMB, TCDB, TFDB) were selected to prepare CMS membranes (CMSMs), providing a systematic study of PIs with different side group functionalization. The resultant CMSMs were characterized by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), Raman spectra, and CO2 absorption measurements. Pure gas (N2, O2, CH4, CO2) and mixed gas (CO2/CH4) permeability tests were also conducted. The resultant CMSMs exhibited attractive gas separation performance. Compared to DMB-based PI, TFDB-based with trifluoromethyl (-CF3) side groups exhibited ultra-high permeability (PCO2 = 14938 Barrer, PO2 = 3146 Barrer) and moderate selectivity (αCO2/CH4 = 20.3, αO2/N2 = 4.5), while CMSMs prepared from PI with chlorine functionalization showed higher gas permeability (PCO2 = 6031 Barrer, PO2 = 1311 Barrer) and selectivity (αCO2/CH4 = 46.2, αO2/N2 = 6.5). The results indicated that side group functionalization on PIs exerts a considerable influence on the gas permeation properties of CMSMs.