In this work, we develop an interpolation theory for metric spaces inspired by the real method of interpolation. These interpolation spaces preserve Lipschitz operators under certain conditions. We also show that this method, valid in metrics spaces, still holds in normed spaces without any algebraic structure required. Furthermore, this interpolation method for metric spaces when applied to normed spaces is equivalent to the K-method, which has been widely studied in the literature. As an application, we interpolate Fréchet sequence spaces.