The Logistic-Map chaotic sequence is often used to scramble and encrypt the digital images.In the former papers,the invalid-keys and the quasi invalid-keys existing in the Logistic-Map have not yet been discussed.If using the invalid-keys or the quasi invalid-keys as the initial value of the Logistic-Map,we can't get the chaotic sequence to scramble the digital images.Furthermore,there are infinite invalid-keys and quasi invalid-keys in the Logistic-Map.So we should take the problems seriously.In this paper,the invalid-keys and the quasi invalid-keys existing in the Logistic-Map chaotic sequence are deeply discussed.Then,an image-scrambling algorithm based on mixed chaotic sequences is proposed.Using this algorithm,the invalidity of the invalidkeys and the quasi invalid-keys is avoided thoroughly.