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We report on the magnetic properties of the layered perovskite $\mathrm{Pb}\mathrm{V}{\mathrm{O}}_{3}$. The results of magnetic susceptibility and specific heat measurements as well as band-structure calculations consistently suggest that the $S=1โˆ•2$ square lattice of vanadium atoms in $\mathrm{Pb}\mathrm{V}{\mathrm{O}}_{3}$ is strongly frustrated due to next-nearest-neighbor antiferromagnetic interactions. The ratio of next-nearest-neighbor $({J}_{2})$ โ€ฆ