In the fast-ignition scheme, very hard x-rays (hereinafter referred to as γ-rays) are generated by Bremsstrahlung radiation from fast electrons. Significant backgrounds were observed around the deuterium-deuterium fusion neutron signals in the experiment in 2010. In this paper the backgrounds were studied in detail, based on Monte Carlo simulations, and they were confirmed to be γ-rays from the target, scattered γ-rays from the experimental bay walls (γ'-rays), and neutrons generated by (γ, n) reactions in either the target vacuum chamber or the diagnostic instruments (γ-n neutrons).