We introduce a novel meshfree Galerkin method for the solution of Reissner–Mindlin plate problems that is written in terms of the primitive variables only (i.e., rotations and transverse displacement) and is devoid of shear-locking. The proposed approach uses linear maximum-entropy basis functions for field variables approximation and is built variationally on a two-field potential energy functional wherein the shear strain, written in terms of the primitive variables, is computed via a volume-averaged nodal projection operator that is constructed from the Kirchhoff constraint of the three-field mixed weak form. The meshfree approximation is constructed over a set of scattered nodes that are obtained from an integration mesh of three-node triangles on which the meshfree stiffness matrix and nodal force vector are numerically integrated. The stability of the method is rendered by adding bubble-like enrichment to the rotation degrees of freedom. Some benchmark problems are presented to demonstrate the accuracy and performance of the proposed method for a wide range of plate thicknesses. © 2018 Elsevier B.V.