A one-dimensional organic–inorganic hybrid perovskite material [3.3.0-dabco]PbBr₃ (1) was synthesized by the reaction of 1,5-diazabicyclo[3.3.0]octane (3.3.0-dabco) with PbBr₂ in concentrated HBr aqueous solution. Differential scanning calorimetry, dielectric measurements, and variable-temperature structural analyses revealed that compound 1 exhibits two successive structural phase transitions from P2₁2₁2₁ to Pbcm at 387 K (T₁) and then to P6/mmc at 436 K (T₂), accompanied by two pairs of dielectric anomalies with a clear one at T₁ and an unobvious one at T₂. In addition, compound 1 shows a robust second harmonic generation (SHG) effect between SHG-OFF and SHG-ON states during its centrosymmetric to non-centrosymmetric symmetry breaking phase transition at T₁.