The nonlinear behaviors of a circular-cylinder piezoelectric power harvester (CCPPH) near resonance are analyzed based on the flow-induced flexural vibration mode. The geometrically-nonlinear effect of the cylinder is studied with considering the in-plane extension incidental to the large deflection. The boundary electric charges generated from two deformation modes, flexure and in-plane extension, were distinguished with each other because the charge corresponding to the latter mode produces no contribution to the output current. Numerical results on output powers show that there are multivaluedness and jump behaviors.