In this work, we use an improved fractional-order logistic map to introduce a new colour image encryption algorithm. By analysing the Lyapunov exponent and the bifurcation diagram, the map provides a wider range and a uniform distribution of data compared to its classical. It also has additional parameters and thus a larger key space, which makes it better in protection and safety against hacker attacks. Our algorithm relies on random input of pixels in order to obtain a different image in each encryption round to ensure greater protection. The algorithm also provides great permutation and diffusion features. The simulation results and security analysis indicate that our scheme has a good impact on encryption and can withstand various attacks, such as statistical attack, differential attack and data loss and noise attacks.