Compared to the previous report on Cu3Bi(SeO3)2O2X(X=Cl,Br) [V. Gnezdilov, (arXiv:1604.04249)],where no dielectric anomaly was observed without magnetic field near TN∼25.6K, we further present the dielectric behaviors without and with magnetic field in Cu3Bi(SeO3)2O2Cl. At zero field H=0, an antiferromagnetic transition from magnetization and specific heat measurements is clearly established at TN, while no dielectric anomaly was observed. Those results are similar to the previous report [V. Gnezdilov, (arXiv:1604.04249)]. Above the critical field Hc∼0.8T, a metamagnetic spin-flip transition from antiferromagnetic to ferrimagnetic order at T∼TN is induced anisotropically only for Hc. Meanwhile, a ferroelectric behavior from dielectric and pyroelectric current measurements is observed below T∼TN; then a corresponding type-II multiferroics emerges above Hc. The key mechanism of the anisotropic spin-flip-induced multiferroicity in Cu3Bi(SeO3)2O2Cl can be ascribed to the breaking of magnetic twofold symmetry in the bc plane above Hc.