A meshless particle-based membrane model is proposed. The particles possess no internal degree of freedom and interact via a potential, which has three different contributions: a short-range repulsive pair potential, an attractive multibody potential, and a curvature potential based on the moving least-squares method. Brownian dynamics simulations are employed to demonstrate that the particles self-assemble into a membrane and to study equilibrium properties, such as bending rigidity, surface tension, line tension, and diffusion constant. The bending rigidity and line tension are shown to depend on different potential parameters and can therefore be varied independently. The finite-size effects of nearly planar membranes are investigated. This model is well suited to study the membrane dynamics with topological changes.