The Ids-Vds properties of a van der Waals cross-junction of few layered MoS2/MoTe2 were investigated, and the physical device parameters were altered in order to transform the conduction mechanism from thermionic emission to interband tunneling. The pristine heterostructure demonstrated rectification behavior of typical p-n junction diodes, because of the p-type and n-type nature of MoTe2 and MoS2, respectively. Lowering the contact resistance between the metal and channel materials, by changing the electrode metals from Au to Pd and Ti, alone did not give rise to carrier conduction through the hetero-interband tunneling between MoTe2 and MoS2. In addition to the reduction in contact resistance, the chemical doping of MoS2 using Benzyl Viologen (BV) achieves hetero-interband tunneling between MoTe2 and MoS2, which probably narrows the depletion layer by degenerating MoS2. The peak-to-valley ratio of the tunneling current of the BV-doped heterostructure of MoS2/MoTe2 is about 4.8, which is comparable to that of the commercially available Si tunneling diode.