A recent trend in the techniques of digital image scrambling encryption is that the algorithms become more and more complex, but their performances are not improved much more. We presented a simple one-dimensional random scrambling method and applied it to image encryption. First, we transformed the image into a one-dimensional vector. And then we did the one-dimensional random scrambling for this vector. Finally, we did reverse transformation on this scrambled vector and got the encrypted image. Compared with Arnold transform, this method is very simple for realizing by software or hardware. It doesn't require iterative computation, and can bring a better result after being executed one time or twice. The experimental results show that the algorithm is effective and has better efficiency and steady scrambling degree than Arnold transform.