We propose a comprehensive delayed HBV model, which not only considers the immune response to both infected cells and viruses and a time delay for the immune system to clear viruses but also incorporates an exposed state and the proliferation of hepatocytes. We prove the positivity and boundedness of solutions and analyze the global stability of two boundary equilibria and then study the local asymptotic stability and Hopf bifurcation of the positive (infection) equilibrium and also the stability of the bifurcating periodic solutions. Moreover, we illustrate how the factors such as the time delay, the immune response to infected cells and viruses, and the proliferation of hepatocytes affect the dynamics of the model by numerical simulation.