Different from traditional massive MIMO arranging ULA only in the azimuth direction, FD-MIMO offers a practical means of realizing massive MIMO in limited space by equipping URA at the base station, which provides extra spatial degree of freedom in elevation domain and eliminates inter-cell interference considerably. Consequently, FD-MIMO draws much attention from both academia and industry for future 5G wireless communication systems. However, the spectral efficiency of URA is lower than its ULA counterpart when adopting the same number of antenna elements due to low resolution caused by the non-uniform distribution of users in the elevation domain. In this article, the concept of NUFD-MIMO is proposed for the first time, which inherits the advantages and is capable of handling the challenges of traditional FD-MIMO. Structured NURA is designed to enhance the spatial resolution of FD-MIMO in the elevation domain and the corresponding two-dimensional precoding is introduced as well. Moreover, some insights on actual NUFD-MIMO implementations in millimeter-wave systems are provided, including non-uniform multi-beam and two-layer phase shifter feeding network. Finally, future work