The theory of real quaternion differential equations has recently received more attention, but significant challenges remain the non-commutativity structure. They have numerous applications throughout engineering and physics. In the present investigation, the Laplace transform approach to solve the linear quaternion differential equations is achieved. Specifically, the process of solving a quaternion different equation is transformed to an algebraic quaternion problem. The Laplace transform makes solving linear ODEs and the related initial value problems much easier. It has two major advantages over the methods discussed in literature. The corresponding initial value problems can be solved without first determining a general solution. More importantly, a particularly powerful feature of this method is the use of the Heaviside functions. It is helpful in solving problems, which is represented by complicated quaternion periodic functions. Copyright (c) 2017 John Wiley & Sons, Ltd.