We develop a neutrino mass model based on \(\Delta \) (27) discrete symmetry by using three Higgs doublets, three right-handed neutrinos, and two \(\Delta \) (27) triplets to explain neutrino oscillation parameters consistent with the Planck cosmological bound on the sum of the three absolute neutrino mass eigenvalues, \(\sum \limits _{i}|m_{i}|<\)  0.12 eV. The detailed numerical analysis is carried out by applying input model parameters and the predicted neutrino oscillation parameters are in agreement with the global neutrino oscillation data for both normal (NH) and inverted (IH) hierarchical model. We also calculate the effective neutrino masses for neutrinoless double beta decay ( \(m_{ee}\) ), tritium beta decay ( \(m_{\beta }\) ), and Jarlskog invariant ( \(J_{CP}\) ) for CP violation as \(m_{ee}\) \(\le \) 30.6 meV, \(m_{\beta }\) \(\le \) 30.5 meV, and \(J_{CP}\) \(\le \) 0.0217 for NH, and \(m_{ee}\) \(\le \) 51.7 meV, \(m_{\beta }\) \(\le \) 51.4 meV, and \(J_{CP}\) \(\le \) 0.0222 for IH.