We analyze the cooperative spontaneous emission of optically excited nanocrystals into surface plasmon polaritons propagating on the surface of a cylindrical metallic nanowire. The spontaneous emission probability of the nanocrystals is obtained by perturbative expansions with and without dipole-dipole interaction among nanocrystals in order to see the cooperative effects. The spontaneous emission probability depends on the radial and axial distributions, as well as on the dipolar orientation of nanocrystals. It is shown that the spontaneous emission probability is strongly influenced by dipole-dipole interaction, axial distribution, and dipolar orientation of nanocrystals for closely spaced nanocrystals.