In [\textit{Y. J. Choie, H. Kim} and \textit{M. I. Knopp}, Math. Z. 219, 71-76 (1995; Zbl 0822.11040)] the authors carried out the construction of a Jacobi cusp form \(f(\tau,z)\) from a pair \(\{h(\tau,z),g(\tau)\}\) consisting of a Jacobi cusp form and an ordinary modular cusp form. There, the coefficients of \(f(\tau,z)\) are defined to be Rankin-Selberg convolution of the Dirichlet series arising as the Mellin transforms of \(h\) and \(g\). This construction is a special case of the general method described by \textit{W. Kohnen} [Math. Z. 207, 659-660 (1991; Zbl 0744.11026)]. In the article under review, the author extends the 1995 result by replacing \(g(\tau)\) with a Jacobi cusp form.