In this paper we derive a strain gradient plate model from the three-dimensional equations of strain gradient linearized elasticity. The deduction is based on the asymptotic analysis with respect of a small real parameter being the thickness of the elastic body we consider. The body is constituted by a second gradient isotropic linearly elastic material. The obtained model is recognized as a strain gradient Reissner-Mindlin plate model. We also provide a mathematical justification of the obtained plate model by means of a variational weak convergence result.