A new donor-acceptor type poly{2-(3,4-didecyloxythiophen-2-yl)-5-[3,4-diphenyl-5-(1,3,4-oxadiazol-2-yl)thiophen-2-yl]-1,3,4-oxadiazole} (P1) has been designed and synthesized starting from thiodiglycolic acid, 1,2-diphenylethane-1,2-dione, and diethyl oxalate through multi-step reactions using precursor polyhydrazide route. The charge-transporting and linear optical property of the polymer has been investigated by cyclic voltammetric, UV-visible, and fluorescence emission spectroscopic studies. The UV-visible absorption spectrum of polymer in thin film form showed maxima at 420 nm. The polymer displayed bluish-green fluorescence both in solution and thin film form. The optical band gap is determined to be 2.27 eV. Third-order nonlinear optical property of the new polymer has been investigated at 532 nm using single beam Z-scan and degenerate four wave mixing (DFWM) techniques with nanosecond laser pulses. The absorptive nonlinearity observed for the polymer P1 is of optical limiting type, which arises due to an "effective" three-photon absorption (3PA) process. The third-order nonlinear optical susceptibility (chi((3))) of the polymer is found to be 0.831 x 10(-12) esu. Both linear and nonlinear optical studies revealed that the new polymer (P1) is a promising material for applications in photonic devices.