An unsymmetrical FDTD subgridding scheme can support complex-valued eigenvalues, which renders an explicit time marching of the FDTD absolutely unstable. However, an unsymmetrical numerical system is often unavoidable to preserve the accuracy of a subgridding scheme. In this work, we develop an accurate FDTD subgridding algorithm suitable for arbitrary subgridding settings with arbitrary grid ratios. Although the resulting system matrix is also unsymmetrical, we develop a time marching method to overcome the stability problem without sacrificing the matrix-free marching of the original FDTD. This method is general, which can be used to make other unsymmetrical subgridding algorithms stable as well. Numerical experiments with various grid ratios have demonstrated the accuracy, stability, and efficiency of the proposed method.