An interchange instability is the most dangerous instability to an open system such as GAMMA10 (Inutake et al 1985 Phys. Rev. Lett.55 939). A line tying is a powerful tool for stabilizing an interchange instability because the magnetic field lines terminate at the conducting ends in an open system. This paper studies the mechanism of the appearance of line tying in an interchange instability by a particle simulation (taking into account the electron inertia along a magnetic field line precisely) and the line-tying effect on the interchange instability in GAMMA10 by a reduced MHD simulation. We have newly found the nonlinear (quasi-linear) stability criterion to an interchange instability with conducting ends. The limiters of Movable Limiter Outside the anchor mirror cell (MLO) installed in GAMMA10 are found to have a stabilization effect on the interchange instability, which is consistent with the experimental results.