Here we show the encapsulation of 35 nm diameter, nearly-spherical, DNA origami by self-assembly of SV40-like (simian virus 40) particles. The self-assembly of this new type of nanoparticles is highly reproducible and efficient. The structure of these particles was determined by cryo-EM. The capsid forms a regular SV40 lattice of T = 7d icosahedral symmetry and the structural features of encapsulated DNA origami are fully visible. These particles are a promising biomaterial for use in various medical applications.