According to the comparability of the nonlinear terms and dispersion terms between the variable coefficient modified Korteweg-de Vries （VCmKdV） equation and constant coefficient KdV-mKdV equation, we transform properly the KdV-mKdV equation with known solutions, transplant its solutions to the VCmKdV equation with unknown solutions, and thus construct the transplantation relation between the solutions of two different equations. Utilizing this transplantation method of solutions, we obtain new exact solutions and solitary wave-like solutions of the coupled VCmKdV system, which is derived from a two-layer fluid model with source or sink. Then we compare the Bcklund transformation and this transplantation method, and analyse the influence of source and sink on the amplitude.