Consider a truncated quiver algebra, where Γ is a finite quiverJis the bilateral ideal ofkΓ generated by the arrows, andk, is a field with characteristic zero. We give another description of a minimal projective resolution of Λ as a Λe-module given in [2] and [8], and using this description we compute the dimensions, as a vector space, of each Hochschild cohomology group of the truncated quiver algebra, in terms of its quiver Γ. We also prove that the Hochschild cohomology ring of Λ is finite dimensional as ak-vector space if and only if Γ has no oriented cycles.