Given a quantum channel Φ in a Hilbert space H, set Φ (ρ) = min ρav =ρ Σ j=1 k πj S (Φ (ρj)), where ρav = Σ j=1 k πj ρj, the minimum is taken over all probability distributions π= {πj } and states ρj in H, and S (ρ) =-Trρ log ρ is the von Neumann entropy of a state ρ. The strong superadditivity conjecture states that ΦΨ (ρ) ≥ Φ (TrK (ρ)) + Ψ (TrH (ρ)) for two channels Φ and Ψ in Hilbert spaces H and K, respectively. We have proved the strong superadditivity conjecture for the quantum depolarizing channel in any dimensions.