We demonstrate a novel method for three-dimensional optical multiple trapping using pure amplitude octagonal almost periodic structures (PAOAPSs). We use a Gaussian beam to diffract through these structures and create a three-dimensional array of trapping spots with the aid of an objective lens. Our device is simple, cost-effective, and easy to fabricate, and it has several advantages over conventional methods for trapping multiple particles. By adjusting the rotation of the PAOAPS and the polarization of the beam, we can simultaneously rotate the trapped particles in both axial and orbital directions. We show that our device achieves an ∼19-fold increase in trapping efficiency compared to a recently introduced method based on an amplitude radial grating. Furthermore, our device transfers about 1/70 of the transmitted beam power to each optical trap, which is much more efficient than a spatial light modulator (SLM).