The invention provides for a volume element (voxel) printing system for printing a three-dimensional object. The system includes a first printhead group having a plurality of first printheads configured to print a first voxel layer on a substrate, and at least one second printhead group having a plurality of second printheads downstream from the first group. The second group is configured to print a subsequent voxel layer on at least part of the first layer. The system also includes an object insertion device configured to insert objects into voids in the voxel layers, and a conveyor to operatively convey the substrate past the printhead groups. Also included is a control system to control and monitor the printhead groups, the object insertion device and the conveyor.