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The radiation trapping effect (RTE) of electrons in the interaction of an ultra-intense laser and a near-critical-density plasma-filled gold cone is numerically investigated by using the particle-in-cell code EPOCH. It is found that, by using the cone, the threshold laser intensity for electron trapping can be significantly decreased. The trapped electrons located behind the laser front and confined near the laser axis oscillate significantly in the transverse direction and emit high-energy $\gamma $ photons in the forward direction. With parameters optimized, a narrow $\gamma $ photon angular distribution and a high-energy conversion efficiency from the laser to the $\gamma $ photons can be obtained. The proposed scheme may offer possibilities to demonstrate the RTE of electrons in experiments at approachable laser intensities and serve as a novel table-top $\gamma $ ray source.