We present a novel method for realizing double-image encryption algorithm by combining the images in different transform domains. Two original images are encrypted into two interim images by fractional Fourier transform and gyrator transform, respectively. The two encrypted images can be obtained by means of the addition and subtraction of the two interim images. This is defined as a double-image sharing scheme, in which the original images are encrypted into two parts. The original images cannot be recovered only with any one of the two interim images. Numerical simulation experiments demonstrate the validity of the algorithm.