Abstract Using a tightly-binding model, we present a Josephson tunneling theory for d-wave superconductivity. Unlike the conventional theory, the interface influence on the wave functions of quasiparticles are taken into account in the model. With the theory, we calculate the temperature dependence of the critical current of Josephson tunneling between YBCO high- T c superconductors along the a-axis. It is shown that the experimental measurements can be excellently explained by the present model with pure d-wave symmetry. Meanwhile, we find that the contribution of the s-wave component, though it may exist, is not significant to the ab-plane tunneling.