A low-density spatial downlink reference signal (LDS-RS) design is proposed for frequency-division duplex (FDD) massive full-dimensional multiple-input multiple-output (FD-MIMO) systems. By exploiting the spatial correlation between the channels of different antennas, this scheme can efficiently reduce the downlink RS overhead and therefore enhances the achievable spectral efficiency significantly. Different from classic RS design methods which utilize the correlation of time/frequency domain and arrange scattered RSs in time/frequency resource block, in our design, RSs are transmitted only on part of antennas in low density. Furthermore, the corresponding channel estimation scheme is also investigated for FDD massive FD-MIMO systems utilizing the proposed LDS-RS design. Simulation results have confirmed that the proposed scheme offers an improved spectral efficiency performance when considering the training overhead in FDD systems.