This paper demonstrates nonlinear theoretical analysis of a flexible rotor system supported by a full-circular journal bearing focusing on the bifurcation phenomenon in the vicinity of the bifurcation point. A third order polynomial approximation model is used for the representation of the oil film force of the journal bearing. The reduced order model, with modes concerning bifurcation, is deduced using the center manifold theory. The dynamical equation in the normal form relating the bifurcation which leads to the oil whirl is obtained using the normal form theory. The influences of various parameters are investigated based on the analysis of a deduced dynamical equation in the normal form. Furthermore, the validity of the derived analytical observation is confirmed by comparing it with the numerically obtained frequency response result.