The Z transform (ZT) theory is newly introduced into the unconditionally stable locally one-dimensional (LOD) FDTD method, in which a complicated treatment of convolution integrals is not required. Through analysis of a surface plasmon waveguide, the accuracy of the ZT-LOD-FDTD is found to be retained for a large time step allowed in an implicit scheme. The computational time is reduced to 25% of that of the traditional explicit ZT-FDTD, maintaining comparable accuracy.