A new donor–acceptor-type conjugated polymer (P1) carrying 3,4-diphenylthiophene, 2,5-dihexyloxybenzene, and 1,3,4-oxadiazole units was synthesized through multistep reactions. The polymer was prepared using a polyhydrazide precursor route. The polymer has a well-defined structure and exhibits good thermal stability, with a decomposition onset temperature in nitrogen of 300 °C. Cyclic voltammetry experiments revealed that the polymer has low-lying LUMO (−3.68 eV) and high-lying HOMO (−5.78 eV) energy levels. The electrochemical band gap was found to be 2.10 eV. The UV-visible absorption spectrum of the polymer presented a maximum at 373 nm, and it displayed bluish-green fluorescence in dilute chloroform solution. The nonlinear optical properties of the new polymer were investigated at 532 nm using the Z-scan technique with nanosecond laser pulses. The polymer exhibited strong optical limiting behavior due to excited state absorption, which was phenomenologically similar to a three-photon absorption (3PA) process. The 3PA coefficient γ was found to be 7 × 10−22 m3/W2. The studies show that the new polymer (P1) is a promising material for developing efficient photonic devices.