In this paper, two kinds of quantum image translation are designed based on FRQI, including global translation and local translation. Firstly, global translation is realized by employing adder modulo N, where all pixels in the image will be moved, and the circuit of right translation is designed. Meanwhile, left translation can also be implemented by using right translation. Complexity analysis shows that the circuits of global translation in this paper have lower complexity and cost less qubits. Secondly, local translation, consisted of single-column translation, multiple-columns translation and translation in the restricted area, is designed by adopting Gray code. In local translation, any parts of pixels in the image can be translated while other pixels remain unchanged. In order to lower complexity when the number of columns needing to be translated are more than one, multiple-columns translation is proposed, which has the approximate complexity with single-column translation. To perform multiple-columns translation, three conditions must be satisfied. In addition, all translations in this paper are cyclic.