We propose a next-to-minimal supersymmetric Standard Model (NMSSM) extended by a $\mathbb{D}_{4}$ discrete flavor symmetry to explain the current neutrino oscillation data within the type I seesaw mechanism. We found that the resulting neutrino mixing matrix is trimaximal. Then, we studied the phenomenology of neutrino parameters for the normal mass hierarchy. In particular, we numerically evaluated the three absolute neutrino mass observables, namely, the sum of absolute neutrino masses $\sum m_{i}$ which is restricted from cosmological observations, the electron neutrino mass $m_{\nu _{e}}$ estimated from single beta decay measurements, and the effective Majorana mass $\left \vert m_{ee}\right \vert $ derived from neutrinoless double beta decay experiments.