We propose a new type of a three-loop induced neutrino mass model with dark matter candidates which are required for the neutrino mass generation. The smallness of neutrino masses can be naturally explained without introducing super heavy particles, namely, much heavier than a TeV scale and quite small couplings as compared to the gauge couplings. We find that as a bonus, the anomaly of the muon anomalous magnetic moment can simultaneously be explained by loop effects of new particles. In our model, there are doubly charged scalar bosons and leptons from isospin doublet fields which give characteristic collider signatures. In particular, the doubly charged scalar bosons can decay into the same-sign dilepton with its chirality of both right-handed or left- and right-handed. This can be a smoking gun signature to identify our model and be useful to distinguish other models with doubly charged scalar bosons at collider experiments.