The well-known Disturbance Decoupling Problem with Stability will be investigated in the case of LPV systems and a sufficient condition for its solvability will be given. By using the concept of parameter varying (A, B)-invariant subspace and parameter varying controllability subspace, this paper investigates the disturbance decoupling problem (DDP) for linear parameter varying (LPV) systems. The parameter dependence in the state matrix of these LPV systems is assumed to be in affine form. The question of stability is addressed in the terms of Lyapunov quadratic stability by using an LMI technique. If certain conditions for the parameter functions and matrices are fulfilled a sufficient condition is given for the solvability of the DDP problem with stability (DDPS).