FeSe0.5Te0.5 single crystals with superconducting critical temperature of 13.5 K are investigated by scanning tunneling microscopy/spectroscopy (STM/STS) measureflents in detail. STM image on the top surface shows an atomically resolved square lattice consisted by white and dark spots with a constant of about 3.73 0.03 which is consistent with the lattice constant 3.78 . The Se and Te atoms with a height difference of about 0.35 are successfully identified since the sizes of the two kinds of atoms are different. The tunneling spectra show very large zero-bias conductance value and asymmetric coherent peaks in the superconducting state. According to the positions of coherence peaks, we determine the superconducting gap 2 = 5.5 meV, and the reduced gap 2/kBTc = 4.9 is larger than the value predicted by the weak-coupling BCS theory. The zero-bias conductance at 1.7 K only have a decrease of about 40% compared with the normal state conductance, which may originate from some scattering and broadening mechanism in the material. This broadening effect will also make the superconducting gap determined by the distance between the coherence peaks larger than the exact gap value. The asymmetric structure of the tunneling spectra near the superconducting gap is induced by the hump on the background. This hump appears at temperature more than twice the superconducting critical temperature. This kind of hump has also been observed in other iron pnictides and needs further investigation. A possible bosonic mode outside the coherence peak with a mode energy of about 5.5 meV is observed in some tunneling spectra, and the ratio between the mode energy and superconducting transition temperature /kBTc 4.7 is roughly consistent with the universal ratio 4.3 in iron-based superconductors. The high-energy background of the spectra beyond the superconducting gaps shows a V-shape feature. The slopes of the differential conductance spectra at high energy are very different in the areas of Te-atom cluster and Se-atom cluster, and the difference extends to the energy of more than 300 meV. The differential conductance mapping has very little information about the quasi-particle interference of the superconducting state, which may result from the other strong scattering mechanism in the sample.