Double radio relics in galaxy clusters are rare phenomena that trace shocks in the outskirts of merging galaxy clusters. We have carried out a spectral and polarization study of the spectacular double relics in the galaxy cluster A3376 using the Giant Metrewave Radio Telescope at 150 and 325 MHz and the Very Large Array at 1400 MHz. The polarization study at 1400 MHz reveals a high degree of polarization (∼30 per cent) and aligned magnetic field vectors (not corrected for Faraday rotation) in the eastern relic. A highly polarized (>60 per cent) filamentary radio source of size ∼300 kpc near the eastern relic and north of the bent-jet radio galaxy is detected for the first time. The western relic is less polarized and does not show aligned magnetic field vectors. The distribution of spectral indices between 325 and 1400 MHz over the radio relics shows steepening from the outer to the inner edges of the relics. The spectral indices of the eastern and the western relics imply Mach numbers in the range 2.2–3.3. Remarkable features such as the inward filament extending from the eastern relic, the highly polarized filament, the complex polarization properties of the western relic and the separation of the brightest cluster galaxy from the intracluster medium by a distance >900 kpc are noticed in the cluster. A comparison with simulated cluster mergers is required to understand the complex properties of the double relics in the context of the merger in A3376. An upper limit [log(P1.4 GHz W Hz−1) < 23.0] on the strength of a Mpc size radio halo in A3376 is estimated.