In this paper a Genetic Algorithm (GA) is proposed to attack an Arabic encrypted text by Vigenere cipher. The frequency of occurrence of Arabic letters has been calculated by using the text of the holy book of Quran, since it has rich language features compared to many other books. The algorithm is tested to find the key letters for different ciphertext sizes and key lengths. The results shows 100% correct letters retrieved from medium size ciphertext and short key length, while 90% of the ciphertext is retrieved from long ciphertext and medium key length, and 82% of the ciphertext is retrieved from long ciphertext and long key.