The encryption of digital images plays a very important role in maintaining privacy and security, in order to protect the people, like witnesses. So, an individual image must be encrypted before it is sent over the Internet to the intended recipient. In this paper, images are encrypted using the rabbit algorithm and the chaotic equation represented by Lévy flight for several reasons, including employing beginning seed number, variance of parameters, and unpredictable random walk direction by making the encryption key more robust through the randomization of the initial vector values. After applying the original and improved rabbit encryption algorithms to the images, the results showed that the proposed Rabbit cipher has shown higher robustness against brute force assaults and larger capability of defending against the statistical cracking. Which has been verified and validated through the use of security metrics are PSNR, MSE, and entropy criteria., The encryption of a 256-size image was achieved in just 3 seconds when the improved Rabbit algorithm has been used, so it will be possible to encrypt video frames in real time because it requires a lesser time and having higher security.