  We consider the three-dimensional incompressible free-boundary
magnetohydrodynamics (MHD) equations in a bounded domain with surface tension
on the boundary. We establish a priori estimate for solutions in the Lagrangian
coordinates with $H^{3.5}$ regularity. To the best of our knowledge, this is
the first result focusing on the incompressible ideal free-boundary MHD
equations with surface tension. It is worth pointing out that the $1/2$-extra
spatial regularity for the flow map $\eta$ is no longer required in this
manuscript thanks to the presence of the surface tension on the boundary.
