Let γ : [0, 1] → S 2 be a non-degenerate curve in R 3 , that is to say, det γ(θ), γ ′ (θ), γ ′′ (θ) = 0. For each θ ∈ [0, 1], let l θ = {tγ(θ) : t ∈ R} and ρ θ : R 3 → l θ be the orthogonal projections. We prove an exceptional set estimate. For any Borel set A ⊂ R 3 and 0 ≤ s ≤ 1, define Es(A)2020 Mathematics Subject Classification. 42B15, 42B20.