Laser-accelerated electrons are promising in producing gamma-photon beams of high peak flux for the study of nuclear photonics, obtaining copious positrons and exploring photon–photon interaction in vacuum. We report on the experimental generation of brilliant gamma-ray beams with not only high photon yield but also low divergence, based on picosecond laser-accelerated electrons. The 120 J 1 ps laser pulse drives self-modulated wakefield acceleration in a high-density gas jet and generates tens-of-MeV electrons with 26 nC and divergence as small as $1.51{}^{\circ}$. These collimated electrons produce gamma-ray photons through bremsstrahlung radiation when transversing a high-Z solid target. We design a high-energy-resolution Compton-scattering spectrometer and find that a total photon number of $2.2\times {10}^9$ is captured within an acceptance angle of $1.1{}^{\circ}$ for photon energies up to $16\;\mathrm{MeV}$. Comparison between the experimental results and Monte Carlo simulations illustrates that the photon beam inherits the small divergence from electrons, corresponding to a total photon number of $2.2\times {10}^{11}$ and a divergence of $7.73{}^{\circ}$.