Aiming to solve the shortcomings of existing chaotic image encryption algorithms, such as small key space and low-security coefficients, we propose a hybrid chaotic image encryption algorithm that integrates wavelet transform with elliptic curve encryption in this paper. Firstly, the two-dimensional grayscale image matrix is transformed into a one-dimensional sequence and then decomposed through a one-dimensional wavelet transform to generate low-frequency and high-frequency coefficient sequences. Subsequently, two random chaotic sequences produced by double iterations of the Logistic chaotic map are utilized to separately perform scrambling and diffusion opera-tions on the low-frequency and high-frequency coefficient sequences. Finally, the processed coefficient sequences along with Logistic chaotic map parameters undergo elliptic curve encryption. Simulation experiments demonstrate that the ciphertexts of multiple test images processed by this algorithm exhibit adjacent pixel correlations close to zero in all directions, with ciphertext information entropy exceeding 7.9993, approaching the ideal value of 8. Both the Number of Pixels Change Rate (NPCR) and Unified Average Changing Intensity (UACI) indicators meet the standards, indicating the algorithm's resistance to differential attacks and its large key space capable of withstanding brute-force attacks, thus demonstrating good security and robustness.