Rapid growth of high quality multimedia (HD) and exchange of data over internet with less storage space and fast processing attracted researchers in the area of compression. Compression is the technique of reducing the image size without degrading the quality of the image. In this work, a commuting matrix with random discrete Fourier transform (DFT) eigenvectors is first constructed. A Random Discrete Fractional Fourier Transform (RDFRFT) kernel matrix with random DFT eigenvectors and eigenvalues is then utilized in image compression. The RDFRFT has an important feature that the magnitude and phase of its transform output are both random. Later, a compression scheme based on random discrete fractional Fourier transform is compared with Discrete Cosine Transform (DCT) and discrete wavelet transform (DWT) based image compression schemes. The given image is subdivided and RDFRFT is applied for each subdivided image to transformed coefficients and reverse order of RDFRFT is applied for reconstruction of original images. The performance of compression scheme based on RDFRFT shows better performance over DFRFT, DCT and DWT based scheme for any multimedia contents. The performance of the proposed scheme is observed on JPEG standard image for prime evaluation parameters such as Peak Signal-to-Noise Ratio (PSNR), Mean Square Error (MSE) and Compression Ratio (CR) for RDFRFT, DCT and DWT based scheme on MATLAB software platform. In addition, the proposed scheme has following advantages: it shows the same computation complexity as DFRFT based system and the feature of additional security can also be incorporated with RDFRFT which is not very significant in case of FRFT and DFRFT based system.