In this article, a memcapacitor bridge circuit consisting of four identical memcapacitors is proposed. With this circuit, we can perform positive, negative and zero synaptic weightings. Weight programming is performed in a memcapacitor bridge circuit, while weight-multiplication processing is performed in a memcapacitor bridge synapse circuit. The current pulse is used in weight programming while the voltage pulse is used in weight-multiplication processing. Simulations are done with a nonlinear drift memcapacitor model. 2013 Elsevier B.V.