We have synthesized a new donor-acceptor (D-A) conjugated polymer containing 3,4-aralkyloxy and alkoxy substituted thiophene and 1,3,4-oxadiazole as donor and acceptor moieties respectively, through precursor polyhydrazide route. The required polyhydrazide was synthesized from 3,4-dihydroxythiophene diester through multistep reaction. The new polymer was characterized by using FTIR, H-1 NMR spectroscopy, followed by Elemental analysis. The average molecular weight of the polymer was determined by Gel Permeation Chromatography. The band gap of the polymer was calculated by using UV-visible and cyclic voltametry. Further, its NLO properties in THF solution were investigated both by the Z-scan and degenerate four-wave mixing (DFWM) techniques using 532 nm, 7 nanosecond laser pulses. The results indicate that they exhibit good optical limiting behavior due to effective two-photon absorption (TPA). Values of the effective TPA coefficient (beta), third-order non-linear optical susceptibility (chi((3))) and figure of merit (F) were calculated. The optical and electrochemical properties reveal that the polymer is a promising candidate for opto-electronic applications.