The effective flexoelectric coefficient and flexoelectric polarization are investigated for a bimesogenic liquid crystal CBC11CB with a twist bend nematic phase (N-tb). The effective flexoelectric coefficients for CBC11CB in the ordinary nematic phase (N) are obtained to be much larger in comparison to conventional calamitics, and is almost twice higher for CBC11CB than that reported for another odd symmetric bimesogen. The flexoelectric polarization (P-f) in the N phase is found to be almost 2.5times higher than in rod-like molecules. Additionally, P-f is obtained to be much larger in the N-tb phase than in the nematic phase.