Zirconium alloys used in nuclear reactor exhibit, under fast neutron flux, a macroscopic deformation even without applied stress called irradiation induced growth. Because of the polycrystalline nature of the material, the local growth of individual grains results in strain incompatibilities yielding to intergranular stresses and thus to local creep. In order to study and understand the influence of the local anisotropic creep on the macroscopic growth behavior, an analytical and a numerical study have been undertaken, using Voigt and self-consistent estimates and also fast Fourier transform simulations. It is shown that the anisotropic local creep has a strong influence on the effective macroscopic growth strain of the polycrystal. Especially, when the deformation is difficult along the ⟨c⟩ axis, a growth enhancement effect is observed. This phenomenon is well explained in the frame of the Voigt estimate using a reduced fibre texture. Computations conducted using a texture representative of the industrial material provide a quantitative confirmation of this enhancement effect. This work demonstrates the significant contribution of the local anisotropic creep to the macroscopic in-reactor growth strain of zirconium alloys.