In this paper, linear quaternion differential equations (LQDEs) with delay attracts our attention. In the light of delayed quaternion matrix exponential and the method of variation of constants, we derive the solutions of homogeneous and nonhomogeneous LQDEs with delay under the assumption of permutation matrices. Further, we investigate the solutions of homogeneous and nonhomogeneous LQDEs with delay without the requirement of permutation matrices. Finally, examples illustrate the validity of the results.