Traditional image encryption technology is usually disadvantaged by low encryption efficiency and inadequate security. In this paper, the time-delay chaos theory was combined with traditional encryption technology to propose a double time-delay chaos-based image encryption algorithm according to the characteristics of image information. First of all, the nonlinear dynamics theory was applied to study the stability of the double time-delay Lorenz system at the equilibrium point and the preconditions for Hopf bifurcation. Then, an analysis was conducted as to the distribution of corresponding characteristic Eq.roots at the equilibrium point, thus obtaining the time-delay critical points for the local asymptotic stability and Hopf bifurcation of the system at the equilibrium point. Secondly, the time-delay critical point was referenced to design the relevant system parameters and time delay of the double time-delay Lorenz system entering the chaotic state, through which the pseudo-random sequence of the chaotic system was determined. Thirdly, the pseudo-random sequence was used for scrambling and diffusion, so as to complete image encryption. Finally, simulation experiment and analysis were conducted for the algorithm from various perspectives such as key space size, key sensitivity, plaintext image sensitivity, plaintext histogram, and so on. According to the research results, the proposed algorithm was capable of producing satisfactory scrambling effect and effective in encrypting and decrypting images without distortion. Meanwhile, the scheme demonstrated not only a certain level of robustness to statistical attack, selective plaintext attack and noise, but also higher stability.