Over the past few years, there has been a rise in the utilization of chaotic encryption algorithms for securing images. The majority of chaos-based encryption algorithms adhere to the conventional model of confusion and diffusion, which typically involves either implementing multiple encryption rounds or employing a single round of intricate encryption to guarantee robust security. However, such kind of approaches reduces the computational efficiency of the encryption process but compromises security. There is a trade-off between security and computational efficiency. Prioritizing security may require high computational processes. To overcome this issue, a key substitution encryption process with discrete wavelet transform (KSP-DWT) is developed in the proposed image encryption technique (IET). Based on KSP-DWT and IET, the abbreviation of the proposed work is used in this paper as KSP-DWT-IET. The proposed KSP-DWT algorithm employs a key scheming technique to update the initial keys and uses a novel substitution method to encrypt digital images of different sizes. Additionally, the integration of DWT can result in the compression of frequency sub-bands of the source image, leading to lower computational overheads without compromising the security of the encryption. The KSP-DWT-IET performs a single encryption round and is highly secure and efficient. The simulation results and security analysis conducted on KSP-DWT-IET confirm its effectiveness in ensuring high-security image encryption while minimizing computational overhead. The proposed encryption technique undergoes various security analyses, including entropy, contrast, correlation, energy, NPCR (Number of Pixel Changes Rate), UACI (Unified Average Change Intensity) and computational complexity. The statistical values obtained for such parameters are 7.9991, 10.9889, 0.0001, 0.0152, 33.6767, and 33.6899, respectively, which indicate that the encryption technique performs very well in terms of security and computational efficiency. The proposed encryption scheme is also analyzed for its computational time in addition to its security. The analysis shows that the scheme can efficiently encrypt images of varying sizes with a high level of security in a short amount of time (i.e., 2 ms). Therefore, it is feasible to use this encryption scheme in real-time applications without causing any significant delays. Moreover, the key space of the proposed encryption scheme is large enough (i.e. Keyspace >2100) to resist the brute force attack.