Nonlinear analysis of complex traffic flow systems can provide a deep understanding of the causes of various traffic phenomena and reduce traffic congestion, and bifurcation analysis is a powerful method for it. In this paper, based on the improved Aw–Rascle model, a new macroscopic traffic flow model is proposed, which takes into account the road factors and driver psychological factor in the curve environment which can effectively simulate many realistic traffic phenomena on curves. The macroscopic traffic flow model on curved road is analyzed by bifurcation, first, it is transformed into a nonlinear dynamical system, then its stability conditions and the existence conditions of bifurcations are derived, and the changes of trajectories near the equilibrium points are described by phase plane. From an equilibrium point, various bifurcation structures describing the nonlinear traffic flow are obtained. In this paper, the influence of different bifurcations on traffic flow is analyzed, and the causes of special traffic phenomena such as stop-and-go and traffic clustering are described using Hopf bifurcation as the starting point of density temporal evolution. The derivation and simulation show that both road factors and driver psychological factor affect the stability of traffic flow on curves, and the study of bifurcation in the curved traffic flow model provides decision support for traffic management.