In this paper we establish some results on a phase-type Lévy risk model with two-sided jumps and a barrier dividend strategy. Following [4] we describe the connection between the ruin problem of the risk model with barrier dividend strategy and the first passage problem of the risk model reflected at its running supremum. Then we give some results for the joint Laplace transform of the upward entrance time and the overshoot for the phase-type jump diffusion reflected at its running supremum. Finally we find some expressions for the Laplace transform of the time of ruin and the expected discounted dividends up to ruin. All our results on the ruin problem are expressed in terms of the solutions to the Cramér-Lundberg equation corresponding to the underlying phase-type jump diffusion.