The virtual element method (VEM) has been shown to perform successfully in various engineering problems. In recent years, it has attracted interest in both mathematics and engineering communities. In this work, a low order virtual element method for 3D contact problems with non-conforming meshes is presented. The contact conditions can be employed on different enforcing strategies. For non-conforming meshes, a node-to-surface enforcement can lead to wrong force distributions at the contact interface. Here, we utilise a mesh adaptivity strategy, which leads to conforming meshes at the contact interface, without introducing new elements. In fact, we take advantage of the useful feature of the virtual element method, which allows to introduce new topological nodes during the simulation. It allows to employ a very simple node-to-node contact formulation for the treatment of contact. This idea was first presented in \cite{Wriggers16} in 2D for small strains and normal contact and was later extended to finite strains and tangential contact. The 2D framework was also successfully extended to 3D problems in \cite{Cihan22}. Thus, this work presents a simple geometrical approach to cut element faces and introduce new nodes in to the existing mesh. Beside a node-to-node contact, this also allows to go one step further and treat the contact pairs as polygonal pair, i.e. surface-to-surface. To verify the new methodology, numerical examples in 3D are shown, including the contact patch test and Hertzian contact problem.