The adhesive contact processes between a rigid spherical tip and substrates with nanogrooves of different sizes have been investigated with a large-scale molecular dynamics simulation method. Influences of the surface grooves on the load-displacement curves, the attractive forces in the loading/unloading processes, and material transfer have been discussed. Results show that compared with the contact between a tip and a smooth surface, the attractive force range becomes larger in the loading process, accompanied by several jumps of the load, and the maximum attractive forces both in the loading and unloading processes are smaller. When the groove depths are the same, the maximum attractive forces in the loading and unloading processes decrease gradually with the increase of the groove width. However, when the groove width becomes close to the contact diameter between the tip and the smooth surface, the maximum attractive force would increase slowly, tending to be close to the case of smooth surface. When the groove width is kept the same, the maximum attractive force in the loading process decreases with the increase of the groove depth, while the maximum attractive force in the unloading process is almost unchanged.