Cryptography is a method for secure communication by hiding information with secret keys so that only authorised users can read and process it. Efficient random sequence generators provide robust cipher design for cryptographic applications; further, these sequences are used for data encryption. In this paper, the highly chaotic nature of hybrid chaos maps and neural network is combined to build a random number generator for cryptographic applications. A custom neural network with a user-defined layer transfer function is built to increase the generator’s randomness. In this work, the two-hybrid chaotic map’s control parameters and iteration value are designed as a layer transfer function to obtain high randomness. Colour image encryption is performed with the extracted sequences and deoxyribonucleic acid encoding technique. Various tests like NIST, attractor test and correlation are applied to the generator to show the degree of randomness. Simulation analysis such as keyspace, key sensitivity, statistical, differential analysis, and chosen-plaintext attack shows the encryption algorithm’s strength. © 2021, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.