In this paper, we study the non-vanishing of the central values of the Rankin-Selberg L-function of two adelic Hilbert primitive forms f\documentclass[12pt]{minimal}
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\begin{document}$$\mathbf{f}$$\end{document} and g\documentclass[12pt]{minimal}
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\begin{document}$$\mathbf{g}$$\end{document}, both of which have varying weight parameter k. We prove that, for sufficiently large k∈2Nn\documentclass[12pt]{minimal}
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\begin{document}$$k\in 2{\mathbb {N}}^n$$\end{document}, there are at least N(k)logcN(k)\documentclass[12pt]{minimal}
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\begin{document}$$\frac{\mathrm{N}(k)}{\log ^c \mathrm{N}(k)}$$\end{document} adelic Hilbert primitive forms f\documentclass[12pt]{minimal}
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\begin{document}$$\mathbf{f}$$\end{document} of weight k for which L(12,f⊗g)\documentclass[12pt]{minimal}
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\begin{document}$$L(\frac{1}{2}, \mathbf{f}\otimes \mathbf{g})$$\end{document} are nonzero.
