In this paper, a transient non-conformal domain decomposition scheme is proposed based on the unconditionally stable Laguerre-FDTD method. Field continuity at the non-conformal domain interface is ensured by applying a mortar-element-like method. A time-derivative Lagrange multiplier is introduced at the domain interface which physically represents the interface current excitation. Simulation results have been presented to demonstrate the accuracy and efficiency of the proposed scheme.