Abstract: Recently, Maire et al. developed a new cell-centered finite-volume Lagrangian method, which greatly eases the problem of spurious grid deformations that have long been troubling cell-centered Lagrangian methods. However, the new method uses only the WWAM approximate Riemann solver in the computation of numerical fluxes, which has much numerical dissipation; moreover, the design of the new method indicates that approximate Riemann solvers in forms other than that of WWAM are not able to be straightforwardly applied to the method. This work successfully applies the MFCAV approximate Riemann solver to Maire et al's method by viewing the MFCAV as a modification of the WWAM. Our numerical tests show that the new method using the MFCAV solver is effective. This study opens a door for applications of Riemann solvers in forms other than that of WWAM to Maire et al's new Lagrangian method.