We investigated the magnetism of vanadium monolayers on a Pd(001) surface. The electronic structure and the magnetic properties of the V/Pd(001) system were determined with the use of the full-potential linearized augmented plane-wave method within the general gradient approximation. Three magnetic configurations were studied: non-, ferro-, and antiferromagnetic. From the total energy calculations, we found that the V/Pd(001) system is the most stable in the antiferromagnetic configuration. The importance of relaxation on the magnetic properties of the systems was also studied. It was found that the Pd(001) surface covered with a V monolayer undergoes considerable relaxation in which the spacing between Pd layers increases in all three magnetic configurations. Contrary to the Pd interlayer spacing, the distance between the V overlayer and the topmost Pd layer is reduced. The interlayer spacing between the V overlayer and the Pd surface layer is the largest for the antiferromagnetic configuration. In the relaxed antiferromagnetic structure, the magnitude of the calculated magnetic moments on the V atoms was $1.31;{mu}_B$. The presence of the vanadium monolayer does not affect the paramagnetic properties of the Pd(001) surface.