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.