We studied the local single-particle tunneling characteristics [as observed with scanning tunnel microscopy (STM)] for N D and S D tunneling, where N is a normal metal, S is a s-wave superconductor, and D is a d-wave superconductor with a {100} | {110} grain boundary. The tunneling Hamiltonian method was used. The self-consistent order parameter is first determined using the quasiclassical Green'sfunction method, and then the tunneling characteristics at various distances from the interface, reectivity of the interface, and temperature are studied. For N D tunneling, a zero-bias conductance peak (ZBCP) occurs near the interface with diminishing magnitude away from it. For S D tunneling, the ZBCP splits to exhibit the gap of the s-wave low-Tc superconducting tunneling tip and there is a range of negative conductance just outside the peaks when the tunneling point is near the grain boundary. The results are compared with those obtained by using a constant order parameter in each grain.