Based on the BTK theory, we investigate the tunneling conductance in uniaxially strained graphene-based normal metal (NG)/barrier (I)/superconductor (SG) junctions. In the present model, we assume that by depositing the conventional superconductor on the top of the uniaxially strained graphene, normal graphene may turn to superconducting graphene with the Cooper pairs formed by the asymmetric Weyl–Dirac electrons, the massless fermions with direction-dependent velocity. The highly asymmetrical velocity, vy/vx≫1, may be created by strain in the zigzag direction near the transition point between gapless and gapped graphene. In the case of highly asymmetrical velocity, we find that the Andreev reflection strongly depends on the direction of strain, and the current perpendicular to the direction of strain can flow through the junction as if there were no barrier. Also, the current parallel to the direction of strain anomalously oscillates as a function of the gate voltage with very high frequency. Our predicted result is quite different from the feature of the quasiparticle tunneling in the unstrained graphene-based NG/I/SG conventional junction. This is because of the presence of the direction-dependent-velocity quasiparticles in the highly strained graphene system.