To explore the possibility of improving the critical current density (Jc) of polycrystalline La1.84Sr0.16CuO4 (LSCO) superconductor ceramics, high density La1.84Sr0.16CuO4 samples have been prepared by means of spark plasma sintering (SPS). Structural and superconducting properties of samples made by different variations of the process have been measured for systematic comparison. The density of the SPS samples can reach up to 98 % of the theoretical density of LSCO, but the critical temperature (Tc) and critical current density (Jc) are suppressed by the process. Subsequent annealing has been applied to improve the properties of the SPS samples. After treatment at 1050 °C, in spite of partial decomposition that was observed on the surface of the samples, the Jc of LSCO was significantly improved. Detailed data as well as assumptions for explaining these results are provided. The SPS technique, coupled with a suitable post-annealing treatment is thereby appearing as a possible methodology to improve the critical current density of polycrystalline high temperature cuprate superconductors.