Based on the random method combining with group and graph theory (RG2), a new chiral (P3221) framework is discovered, which can be considered as the second crystalline allotrope of C3N4 with mixed sp2 and sp3 bonding features similar to the previously synthesized P43212 phase [Physical Review B, 94, 094,106, 2016]. P3221 is both dynamically and mechanically stable, and it is energetically more favorable than the superhard and dense α-phase and β-phase at ambient conditions. The calculated band structures show that P43212 and P3221 are indirect band gap insulators with energy gaps of 3.452 eV and 3.542 eV and their Vicker's hardness are confirmed to be 10. 98 GPa and 22.79 GPa, respectively. It is interesting that the simulated E-P and E-V curves show that P3221 will be more favorable than P43212 after 19 GPa and it possesses an opportunity to survive within a certain volume interval.