Semiconductor nanowires/films with strong spin-orbit coupling and proximity-induced s-wave superconductivity in an external magnetic field have been the most promising settings for approaches towards experimental evidence of topological Majorana zero-energy bound state. We investigate the effect of tilting the magnetic field relative to the spin-orbit coupling direction using the recursive Green's function method and provide a numerical simulation of the critical angle, at which the topological states disappear. Meanwhile, The dependence of the Majorana zero energy states and the minigaps on various physics parameters (Zeeman field, chemical potential, spin-orbit coupling strength) is characterized. We find the minigaps depend strongly on the spin-orbit coupling strength. We also obtain the differential conductance characteristic of a junction with a normal wire for different tilting angles and propose a qualitative change of the dependence of the zero-energy differential conductance on the tunnel barrier strength at the critical angle as a criterion for establishing the topological nature of the observed signal.