<p>To tackle the challenge that single-dose vaccination is difficult to control diseases over a prolonged period due to the attenuation of the effectiveness of vaccines, this study focuses on the double-dose vaccination strategy. It constructs a dynamic model of two-strain infectious diseases with double-dose vaccination on complex networks. Firstly, the basic reproduction number and the invasion reproduction number of the model are calculated. The global asymptotic stability of the disease-free equilibrium, the strain-dominant equilibria, and the coexistence equilibrium are proved by using the Lyapunov function method and LaSalle’s invariance principle. The numerical simulations verify the theoretical conclusions. The results show that the vaccination can effectively inhibit the spread of the disease, and the effect of the double-dose vaccination strategy is significantly better than that of the single-dose vaccination, which can more effectively reduce the peak of infection and control the size of the epidemic. This study provides a theoretical basis for the prevention and control of two-strain infectious diseases, highlighting the importance of optimizing vaccine protection effectiveness and exploring multiple vaccination strategies.</p>