We propose to understand the mixing angles and CP-violating phases from the Delta(48) family symmetry combined with the generalized CP symmetry. A model-independent analysis is performed by scanning all the possible symmetry breaking chains. We find a new mixing pattern with only one free parameter, excellent agreement with the observed mixing angles can be achieved and all the CP-violating phases are predicted to take nontrivial values. This mixing pattern is testable in the near future neutrino oscillation and neutrinoless double-beta decay experiments. Finally, a flavor model is constructed to realize this mixing pattern.