We explore the gamma radiation characteristics of double-layer targets driven by nanosecond/picosecond two-beam lasers based on the Shenguang II upgrade laser facility. A nanosecond laser is used to interact with a thin film target to generate a large-scale near-critical density plasma. Further, a picosecond laser interacts with the plasma to generate high-energy electrons. The high-energy electrons pass through a 2 mm thick Au target to generate gamma rays via bremsstrahlung. Subsequently, the experiments measure the gamma energy spectra in different directions and gamma doses outside the target chamber. It is found that the gamma radiation is concentrated in the picosecond laser propagating direction with a small divergence angle, and the high-energy parts of the gamma rays are enhanced in this direction as well. The design of the double-layer target can improve the energy coupling efficiency of the picosecond beam and plasma, increase the temperature and number of high-energy electrons, and facilitate the concentration of high-energy gamma radiation in the propagating direction of the picosecond laser beam. Furthermore, the single-shot maximum dose of gamma radiation, which has energy higher than 50 keV and is measured at 1.25 m from the target outside the target chamber, is 277 μGy. Results of the present study could be considered as references for the shielding and application of gamma radiation.