From the measurements of magnetic susceptibility, heat capacity, magnetization and EPR, the magnetism of the organic radical crystal of 1,3,5-triphenyl-6-oxoverdazyl is revealed to be descrived by a two-dimensional quantum Heisenberg antiferromagnet with the effective intra-plane exchange interaction J/k(B)= -4.3 K. The appearance of weak ferromagnetic moment is observed below 5.4 K. The magnetic susceptibility, however, shows its broad maximum around 2 K and decrease toward the low temperatures. These results are shown to be described by a four-sublattice model with two Dzyaloshinsky-Moriya vectors of opposite sign on the ac-plane. A proposal is made for crystal symmetry in which weak ferromagnetic moment is stabilized without direct ferromagnetic interactions.