NectarCAM is a camera proposed for the medium-sized telescopes of the Cherenkov Telescope Array (CTA) covering the central energy range of ~100 GeV to ~30 TeV. It has a modular design and is based on the NECTAr chip, at the heart of which is a GHz sampling Switched Capacitor Array and a 12-bit Analog to Digital converter. The camera will be equipped with 265 7-photomultiplier modules, covering a field of view of 8 degrees. Each module includes the photomultiplier bases, high voltage supply, pre-amplifier, trigger, readout and Ethernet transceiver. The recorded events last between a few nanoseconds and tens of nanoseconds. The camera trigger will be flexible so as to minimize the read-out dead-time of the NECTAr chips. NectarCAM is designed to sustain a data rate of more than 4 kHz with less than 5% dead time. The camera concept, the design and tests of the various subcomponents and results of thermal and electrical prototypes are presented. The design includes the mechanical structure, cooling of the electronics, read-out, clock distribution, slow control, data-acquisition, triggering, monitoring and services.