We present an experimental study of S−N−S junctions, with N being a quantum spin Hall insulator made of InAs/GaSb. A front gate is used to vary the Fermi level into the minigap, where helical edge modes exist [Phys. Rev. Lett. 107, 136603 (2011)]. In this regime we observe a ∼2e2/h Andreev conductance peak, consistent with a perfect Andreev reflection on the helical edge modes predicted by theories. The peak diminishes under a small applied magnetic field due to the breaking of time-reversal symmetry. This work thus demonstrates the helical property of the edge modes in a quantum spin Hall insulator.