Spin waves are propagating disturbances in the magnetization of magnetic materials. One of their interesting properties is the nonreciprocity, exhibiting that their amplitude depends on the magnetization direction. Nonreciprocity in spin waves is of great interest in both fundamental science and applications, as it offers an extra knob to control the flow of waves for the technological fields of logics and switch applications. We show a high nonreciprocity in spin waves from Ta/Py bilayer systems with out-of-plane magnetic fields. The nonreciprocity depends on the thickness of Ta underlayer which is found to induce an interfacial anisotropy. The origin of observed high nonreciprocity is twofold; different polarities of the in-plane magnetization due to different angles of canted out-of-plane anisotropy and the spin pumping effect at the Ta/Py interface. Our findings provide an opportunity to engineer highly efficient nonreciprocal spin wave based applications such as nonreciprocal microwave devices, magnonic logic gates, and information transports.