Analogous to graphite, hexagonal boron nitride (h-BN) has a layered structure composed of boron and nitrogen atoms that are alternatively bond to each other in a honeycomb array. As the layers are held together by weak van der Waals forces, h-BN thin films can be grown on surfaces of various metal crystals in a layer-by-layer manner, which is again similar to graphene sheets and thus attracts a lot of research interests. In this work, scanning tunneling microscope and spectroscope (STM and STS) were applied to the study of an h-BN thin film with a thickness of about 10 nm grown on Cu foil by means of chemical vapor deposition. X-ray diffraction from the Cu foil shows only one strong peak of Cu(200) in the angle range of 40-60, indicating that the Cu foil is mainly Cu(100). After sufficient annealing in an UHV chamber, the h-BN film sample is transferred to a cooling stage (77 K) for STM/STS measurement. Its high quality is confirmed by a large-scale STM scan that shows an atomically flat topography. A series of dI/dV data taken within varied energy windows all exhibit similar U shapes but with different bottom widths that monotonously decrease with the sweeping energy window. The dI/dV curve taken in the energy window of [-1 V, +1 V] even shows no energy gap in spite that h-BN film is insulating with a quite large energy gap of around 6 eV, as observed in a large-energy-window dI/dV curve (from -5 V to +5 V). These results indicate that the STM images reflect the spatial distribution of tunneling barriers between Cu(100) substrate and STM tip, rather than the local density of states of the h-BN surface. At high sample biases (from 4 V to 1 V), STM images exhibit an electronic modulation pattern with short range order. The modulation pattern displays a substructure in low-bias STM images (less than 100 mV), which finally turns to the (11) lattice of h-BN surface when the sample bias is extremely lowered to 3 mV. It is found that the electronic modulation pattern cannot be fully reproduced by superimposing hexagonal BN lattice on tetragonal Cu(100) lattice, no matter what their relative in-plane crystal orientation is. This implies that the electronic modulation pattern in the STM images is not a Mori pattern due to lattice mismatch. We speculate that it may originate from spatial distribution of tunneling barrier induced by adsorption of H, B and/or N atoms on the Cu(100) surface in the CVD growth process.