In this paper, we consider projective deformation of the geodesic system of Finsler spaces by holonomy invariant functions. Starting with a Finsler spray S and a holonomy invariant function P, we investigate the metrizability property of the projective deformation ̃S = S − 2λPC. We prove that for any holonomy invariant nontrivial function P and for almost every value λ ∈ R, such deformation is not Finsler metrizable. We identify the cases where such deformation can lead to a metrizable spray. In these cases, the holonomy invariant function P is necessarily one of the principal curvatures of the geodesic structure.