Organo-soluble aromatic polyimides with good comprehensive properties are favorable for insulating layer material applications in flexible copper-clad laminates. A novel aromatic diamine, bis( N-4-amine-phenyl)-3,3′-bicarbazole (BCZDA) was firstly successfully synthesized. The structure of BCZDA was definitely confirmed via Fourier transform infrared and 1H-NMR spectroscopy and elemental analysis. Then a series of soluble polyimides were prepared from BCZDA and the diamine containing phthalazinone moiety as coreactant by one-pot solution copolycondensation with two kinds of anhydrides, 3,3′,4,4′-benzophenonetetracarboxylic dianhydride and 2-bis[4-(3,4- dicarboxyphenoxy) phenyl] propane dianhydride in sulfolane. Experimental results indicated that all the copolyimides having the glass transition temperature in range of 295 to 304 °C exhibited good solubility in N-methyl-2-pyrrolidinone (NMP), m-cresol, and N, N-dimethyl acetamide (DMAc). Their onset temperatures at 5% weight loss were all higher than 505 °C in nitrogen. Their flexible films cast in NMP exhibited good adhesive property (2.32–3.42 N mm−1) to copper foil and had good mechanical properties with the tensile strength of 69.5–79.3 MPa, elongation to break of 16–23% , and tensile modulus of 1.2–1.5 GPa. The copolyimides possessed dielectric constants of 3.08–3.26 (100 kHz) and low water absorption in the range of 0.92–1.06%, indicating that these obtained copolyimides are good candidates for the fields of microelectronics.