Mesh generation is known to be a bottleneck in modern digitalised industrial production workflows. It often requires excessive amount of human labour to convert the geometric model from computer-aided design (CAD) to its discretised counterpart in computer-aided engineering (CAE) for numerical simulations. This is because a CAD model, typically described by non--uniform rational B--splines (NURBS), usually contains multiscale features that require manipulations, such as de-featuring, to avoid an extreme locally refined mesh. This is undesirable for most numerical simulations, especially those using explicit time integrators. Automatic feature detection and removal have been studied for decades, though not yet fully achieved. An important reason for this is that the effect of the de--featuring is unpredictable, especially for problems involving multi--physics. The NURBS--enhanced FEM (NEFEM) has been proposed to address this problem. NEFEM separates concepts of geometric description and solution approximation. The NURBS description of the model, directly available from the CAD data, is used to describe the geometry, whereas standard polynomials are used for the functional approximation. This enables the NEFEM element to describe the exact geometry given by a CAD model, eliminating the need for de--featuring and the need for small elements where they are not required. In this work, a hierarchical mesh generation scheme is developed to generate surface and volume meshes for NEFEM in three dimensions. Starting from the CAD model, a standard surface mesh is initially generated. It is then remeshed to create NEFEM surface elements traversing geometric entities with sizes complying with the user specification. The NEFEM surface mesh is used as the discretised boundary to grow NEFEM volume elements. Examples will be presented to demonstrate the benefits brought by this new mesh generation framework.