Tungsten ditelluride (WTe₂), as one of material candidates in the family of type-II Weyl semimetals, exhibits many exotic properties, such as anisotropic chiral anomaly. Due to the intrinsic topological band structure and tilted Weyl cone in WTe₂, it has been predicted that unconventional superconducting properties will emerge when WTe₂ enters to superconducting phase. In this work, we report the observation of superconductivity in the type-II Weyl semimetal WTe₂ based on WTe₂/NbSe₂ heterostructure induced by proximity effect. We find a long coherence length along c axis of WTe₂. Furthermore, we observe anomalous oscillations of the differential resistance spectrum during the transition from superconducting to normal state. Theoretical calculations indicate that the staged change in the differential resistance spectrum can be associated with anomalous density of states in superconducting state and reveals that such a sub-gap anomaly is the intrinsic property of WTe₂ in superconducting state induced by the proximity effect. Our findings can enrich the understanding of superconductivity mechanism in type-II Weyl semimetal and pave the way for their future applications in topological quantum computing.