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La 1.5 Sr 0.5 NiO 4 is well known to have a colossal dielectric constant (ε R > 10 7 ). The La 1.5 Sr 0.5 NiO 4 nanoparticle powder was prepared by a combinational method of solid state reaction and high-energy ball milling. Magnetic measurements show that the material has a very small magnetic moment and paramagnetic characteristic at room temperature. The mixture of the nanoparticle powder (40% vol.) and paraffin (60% vol.) coated in the form of flat layers of different thicknesses (t) exhibits strong microwave absorption resonances in the 4-18 GHz range. The reflection loss (RL) decreases with t and reaches down to -36.7 dB for t = 3.0 mm. The impedance matching (|Z| = Z 0 = 377 Ω), rather than the phase matching mechanism, is found responsible for the resonance observed in the samples with 1 < t ≤ 3.0 mm. Further increase of the thickness leads to |Z| > Z 0 at all frequencies and a reduced absorption. The influence of non-metal backing is also discussed. Our observation suggests that La 1.5 Sr 0.5 NiO 4 nanoparticles could be used as good fillers for high performance radar absorbing material.