Because images are vulnerable to external attacks in the process of network transmission and traditional image encryption algorithms have limitations such as long encryption time, insufficient entropy or poor diffusion of cipher image information when encrypting color images, a fast image encryption algorithm based on logistics-sine-cosine mapping is proposed. The algorithm first generates five sets of encrypted sequences from the logistics-sine-cosine mapping, then uses the order of the encryption sequence to scramble the image pixels and designs a new pixel diffusion network to further improve the key sensitivity and plain-image sensitivity of the encryption algorithm. Finally, in a series of security analysis experiments, the experimental image Lena was tested 100 times, and the average encryption time was 0.479 s. The average value of the information entropy, pixel change rate and uniform average change intensity of the cipher image reached 7.9994, 99.62% and 33.48%, respectively. The experimental results show that the fast image encryption algorithm based on logistics-sine-cosine mapping takes less time to encrypt, and the cipher image has good information entropy and diffusivity. It is a safe and effective fast image encryption algorithm.