A three-dimensional (3D) inkjet printer is configured to build up an object by printing a series of layers and stacking them to form the object. In order to speed printing, drying of each layer is accelerated by using a pressure differential to extract liquid vehicle from the ink, and by moving the printed layer away from the inkjet print heads before drying so that the inkjet print heads may print the next layer. The dried printed layer may also be conditioned and/or cured. Dried printed layers are stacked at a build station to assemble the finished object.