We analyze the delay performance of traffic dispersion in millimeter-wave (mm-wave) communications, where Nakagami-m fading channel is considered. To apply (mm, +)algebra network calculus in wireless communications, we develop a closed-form expression based on moment generating function (MGF), which characterizes the stochastic service process by staying in the bit domain, rather than transferring to the SNR domain. Subsequently, for traffic dispersion with mm-wave, we derive probabilistic delay bounds and effective capacity based on the obtained MGF of the cumulative service process. Besides, the impacts of several factors, e.g., the number of independent path, system gain (including antenna gain and adopted radio frequency) or Nakagami parameter, on the delay performance are studied. We not only comprehensively study the delay performance of traffic dispersion with mm-wave, but also demonstrate the feasibility and tractability of performance analysis.