This paper investigates the global exponential stability of homogeneous impulsive positive delay systems of degree one. By using the max-separable Lyapunov functions, a sufficient criterion is obtained for exponential stability of continuous-time homogeneous impulsive positive delay systems of degree one. We also provide the corresponding counterpart for discrete-time homogeneous impulsive positive delay systems of degree one. Our results show that a stable impulse-free system can keep its original stability property under certain destabilising impulsive perturbations. It should be noted that it's the first time that the exponential stability results for homogeneous impulsive positive delay systems of degree one are given. Numerical examples are provided to demonstrate the effectiveness of the derived results.