A liquid-vapor phase change is an efficient process to transfer thermal energy and has been used in many industrial applications. To enhance the liquid-vapor phase-change heat transfer, nanoengineered materials, such as nanostructured surfaces, have been experimentally and numerically investigated so far. Nevertheless, understating how the nanostructured surfaces influence evaporation has not been sufficient. For the evaporation of water droplets, some experimental studies employed complex geometry nanostructured surfaces, such as needle shapes or porous structures in unstructured forms. Those studies showed that nanostructured surfaces could enhance droplet evaporation. Yet, the microscopic evaporation mechanism has not been comprehensively understood. In addition, we have not been able to predict evaporation characteristics based on any physical models. Because of this, the present study employs periodic nanostructured surfaces. With electron beam lithography, we fabricate nanoscale cubic pillars in a periodic configuration on silicon specimens. The pillars are approximately 100 nm in width and height. Gap openings between the pillars are also approximately 100 nm. With a goniometer, we evaluate the contact angle and radius of water droplets on the specimens. On a flat surface, a sessile droplet evaporates in the following evaporation modes: a constant contact radius (CCR) mode and consequently a constant contact angle (CCA) mode. However, on nanostructured surfaces, water droplets can spread. With respect to flat surfaces, it shows better wettability. Based on a modified Wenzel equation for periodic square pillars, we assume that the Wenzel state is realized on the nanostructured surfaces. Furthermore, the contact line of the droplet is effectively pinned on the nanostructured surface. We confirm that the nanostructured surfaces can reduce the lifetime of an evaporating droplet by approximately half. A conventional physical model for flat surfaces cannot predict the characteristics of the evaporation droplet on the nanostructured surfaces. In addition, the nanostructured surfaces induce a unique evaporation mode between the CCR and CCA modes, hereafter referred to as transition mode. In the transition mode, the contact line slowly recedes together with the transient change in contact angle during the evaporation process, and the dynamics are different from the CCR and CCA modes.