One of the most straightforward extensions to the Standard Model is the $U(1)_{B-L}$ model based on the gauge group $SU(3)_C \times SU(2)_L
\times U(1)_Y \times U(1)_{B-L}$. This model contains three heavy Right-Handed (RH) neutrinos, essential for anomaly cancellation and preserving
gauge invariance. The model is attractive due to its relatively simple theoretical structure, and the crucial test of the model is the detection
of the new heavy neutral $Z'$ gauge boson, the heavy-neutrinos $\nu_R$, and the new Higgs boson $H$. With these motivations, we carried out a study
on the $Z'$ resonance and heavy-neutrino pair production at the future muon collider through the process $\mu^+\mu^- \to Z' \to \nu_R \nu_R \to l^{\pm}W^{\mp}l^{\mp}W^{\pm}$
with the subsequent decay of $\nu_R$ to pairs of $l^{\pm}W^{\mp}$ with $l=e, \mu$.