Abstract A strain-gradient crystal plasticity constitutive model was developed in order to predict the Hall-Petch behavior ofa Ni-base polycrystalline superalloy. The constitutive model involves statistically stored dislocation and geometrically necessarydislocation densities, which were incorporated into the Bailey-Hirsch type flow stress equation with six strength interactioncoefficients. A strain-gradient term (called slip-system lattice incompatibility) developed by Acharya was used to calculate thegeometrically necessary dislocation density. The description of Kocks-Argon-Ashby type thermally activated strain rate was alsoused to represent the shear rate of an individual slip system. The constitutive model was implemented in a user materialsubroutine for crystal plasticity finite element method simulations. The grain size dependence of the flow stress (viz., the Hall-Petch behavior) was predicted for a Ni-base polycrystalline superalloy NIMONIC PE16. Simulation results showed that thepresent constitutive model fairly reasonably predicts 0.2 %-offset yield stresses in a limited range of the grain size.Key wordscrystal plasticity, strain gradient plasticity, finite element method, hall-petch relation, polycrystal.