Full-potential linearized augmented plane wave (FP-LAPW) method with the generalized gradient approximation (GGA) for the exchange-correlation potential has been applied for the study of structural, elastic and electronic properties of the newly synthesized nitrogen-containing perovskite-like superconductor ZnNNi3. The optimized lattice parameter, independent elastic constants (C11, C12 and C44), bulk modulus B, compressibility betta, and shear modulus G are evaluated. The band structure, total and site- projected l- decomposed DOSs, the shape of the Fermi surface, the Sommerfeld coefficient and the molar Pauli paramagnetic susceptibility for this novel anti-perovskite are obtained and analyzed in comparison with related anti-perovskites ZnCNi3 and MgCNi3
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