This Letter proposes a random plasmonic laser in the metal-insulator-metal (MIM) structure, in which the dielectric core with gain is dispersed with circular dielectric nanoscatterers. The numerical results from finite-difference time-domain simulation indicate that scattering by the randomly distributed dielectric nanoscatterers in the MIM waveguide provides feedback to the random laser with surface plasmon. The design bypasses the requirement of a distributed feedback structure for the plasmonic waveguide-based nanolasers, which is challenging and expensive in fabrication. Additionally, the MIM structure makes this type of random laser easily applicable to nanoscale integrated photonic devices and circuits.