We prove the local-in-time existence and uniqueness of solutions to the free-boundary problem in ideal compressible MHD with surface tension by a suitable modification of the Nash-Moser iteration scheme. The main ingredients in proving the convergence of the scheme are tame estimates and unique solvability of the linearized problem in the anisotropic weighted Sobolev spaces. In order to derive the tame estimates, we make full use of the boundary regularity enhanced from the surface tension. The unique solution of the linearized problem is constructed by designing its suitable artificial regularization and passing to the limit as the regularization parameter tends to zero. In the end of the talk, we also briefly discuss an analogous local well-posedness result for MHD contact discontinuities with surface tension. The results presented in the talk are the joint work with Tao Wang (Wuhan University).