The dispersion properties of surface plasmon polaritons (SPPs) during propagation on metal wires with a dielectric coating in the terahertz frequency range were investigated theoretically. An analytical expression was obtained for a pulsed electric field using the solution of Maxwell equations taking into account high-order dispersion terms. The influence of the dielectric coating on the distortion of the pulse shape was investigated. Unlike uncoated wire, the propagation of surface plasmon pulses along a coated wire is highly dispersive. It was shown that the coating leads to the appearance of a long-chirped signal with a propagation of only a few millimeters, i.e., when a terahertz pulse propagates along a coated wire, it acquires a long oscillatory tail, the frequency of which depends on time.