A color image encryption method is proposed. The method uses discrete fractional random transform (DFRNT) and Arnold transform (AT) to encrypt in the luminance hue saturation color space. A color image is converted from the standard red-green-blue (RGB) space to luminance hue saturation space . The luminance component is encrypted by a method DFRNT transform, which encrypts the pixel value and the pixel position simultaneously. The hue and saturation components are encrypted using an Arnold scrambling method that scrambling pixels. Compared with the traditional double-random-phase encoding, the DFRNT encryption method can save storage space of the encryption key. At the same time, it is as safe as the traditional dual random phase coding. The fractional order of the DFRNT, the random matrix and the iteration numbers of Arnold transform are used as the encryption keys of the algorithm. The performance of the cryptographic algorithm is analyzed against the variation in fractional order, the change of Arnold transform iteration number, known-plaintext attack, noise addition and occlusion of the encrypted image. The test results show the feasibility and effectiveness of the scheme.