This disclosure provides an improved system for culturing human pluripotent stem cells. Traditionally, pluripotent stem cells are cultured on a layer of mouse embryonic fibroblast feeder cells to prevent them from differentiating. In the system described here, the role of feeder cells is replaced by defined components added to the culture environment that support rapid proliferation without differentiation. The medium contains an isotonic buffer, a blend of essential nutrients such as protein and lipids, and an effective growth factor or combination of factors that promote proliferation while inhibiting differentiation. Culturing human embryonic stem cells in fresh medium on an extracellular matrix according to this invention causes the cells to expand surprisingly rapidly, while retaining the ability to differentiate into cells representing all three embryonic germ layers. This new culture system allows for bulk proliferation of pPS cells for commercial production of important products for use in drug screening and human therapy.