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In this letter, to model surface plasmon polaritons, trapezoidal recursive convolution-locally 1-D finite-difference time-domain (TRC-LOD-FDTD) equations at metal-dielectric interface are derived using the Drude model. The integral form of Maxwell's curl equation for magnetic field is applied on Yee's lattice to establish boundary conditions. Then, the TRC technique is used for the analysis of the Drude model. The advantages of our presented method include removing the restriction of the field's confinement to the interface and simple calculation of the TRC-LOD-FDTD equations at the metal-dielectric interface.