In this paper, a resistive-capacitive-shunted Josephson junction with linear delayed feedback is considered. The stability of trivial solution of the controlled system is analyzed using nonlinear dynamics theory, and the theoretical results show that the stable trivial solution of the system will lose its stability via Hopf bifurcation as control parameter varies. The critical parameter condition of Hopf bifurcation is also derived. Numerical analysis of the controlled system is carried out under different parameter conditions, and the results show that the stable periodic solution generated by supercritical Hopf bifurcation may transit to chaos gradually through a process of symmetry-breaking bifurcation and period-doubling bifurcation.