A　novel　weakly　conditionally　stable　finite-difference　time-domain　(FDTD)　method　that　is　extremely　useful　for　problems　with　very　fine　structures　over　a　large　computational　domain　in　one　or　two　directions　is　presented.　The　time　step　in　this　method　is　only　determined　by　the　largest　space　discretization.　The　weakly　conditional　stability　and　the　dispersion　relation　of　the　proposed　novel　weakly　conditionally　stable　(NWCS)-FDTD　method　are　presented　analytically.　Compared　with　the　alternating-direction　implicit　(ADI)-FDTD　method,　this　NWCS-FDTD　method　has　higher　accuracy,　especially　for　larger　time-step　size.　At　each　time　step,　the　NWCS-FDTD　method　requires　the　solution　of　four　tridiagonal　matrices　and　four　explicit　updates.　While　maintaining　the　same　size　of　the　time　step,　the　CPU　time　for　this　weakly　conditionally　stable　FDTD　method　can　be　reduced　to　about　two-thirds　of　that　for　the　ADI-FDTD　scheme.　The　numerical　performance　of　the　proposed　NWCS-FDTD　method　over　the　ADI-FDTD　method　is　demonstrated　through　numerical　examples.