A lot of research has shown that the strength of nanoparticle composites increases first and then decreases with the decrease of particle size when particle size is at nanoscale, which is the so-called positive-inverse Hall–Petch effects, or called the strengthening-softening characteristic. In this paper, the strengthening-softening behavior of cylindrical nanoparticle composites with periodic distribution of particles is studied. By selecting the representative single cylindrical cell model, the mechanic’s solution is obtained strictly by using the strain gradient viscoelastic theory established previously by the present authors. The results clearly show the strengthening-softening behavior of the nanoparticle composite. In the process of solution, first, the strain gradient elasticity theory is used to strictly solve the problem of the cylindrical cell under uniform external pressure. Then, using the correspondence principle of the strain gradient viscoelastic theory, the solution for the strain gradient viscoelastic theory is obtained through Laplace inversion transformation, and its dependence on the time-space two-scale parameters is analyzed. The results showed a significant positive-inverse Hall–Petch effects.