Magnetic properties of a S=3/2 honeycomb antiferromagnet Bi3Mn4O12(NO3) are discussed. Susceptibility and specific heat measurements showed that this system is free from a long range ordering at least down to 0.4 K in a low magnetic field because of the geometrical frustration caused by the competition between the nearest and the next nearest interactions. On the other hand, magnetization and neutron diffraction studies revealed a field-induced long range ordering at around 10 K and 6 T.