We investigate in detail a model that contains an additional SU(2) singlet and triplet scalar fields than the Standard Model (SM). This allows the radiative generation of Majorana neutrino masses at two-loop order with the help of doubly charged Higgs bosons that arise from the extended Higgs sector. The phenomenology of the Higgs and neutrino sectors of the model is studied. We give the analytical form of the masses of scalar and pseudoscalar bosons and their mixings, and the structure of the active neutrino mass matrix. It is found that the model accommodates only normal neutrino mass hierarchy, and that there is a large parameter space where the doubly charged Higgs can be observed at the Large Hadron Collider (LHC), thereby making it testable at the LHC. Furthermore, the neutrino-less double beta (0νββ) decays arise predominantly from exchange processes involving the doubly charged Higgs, whose existence is thus unmistakable if 0νββ decays are observed. The production and decays of the doubly charged Higgs are analyzed, and distinct and distinguishing signals are discussed.