This paper aims to improves the chaotic behavior of classical logistic chaotic map for image encryption. First, this classical technique was enhanced, and the effectiveness of the improved technique was verified by the bifurcation diagram and Lyapunov exponent, in comparison to the classical technique. On this basis, an efficient tweakable image encryption algorithm was proposed to protect the security of digital image transmission. The proposed algorithm adopts a confusion-diffusion architecture. With the aid of the tweak, each original image is encrypted as multiple different images using the same secret key-stream. The experimental results prove that the proposed algorithm, despite its simplicity, can withstand several types of attacks through image encryption. The research results shed new light on the data security in the transmission of digital images.