For the obstacle problem involving a convex fully nonlinear elliptic operator, we show that singular set in free boundary stratifies. The top stratum is locally covered by $C^{1,\alpha}$ manifold, and lower strata are $C^{1,\log^\varepsilon}$ manifolds. This recovers some of recent regularity results due to Colombo–Spolaor–Velichkov (2018) Figalli–Serra (2019) when operator Laplacian.