The Schneider CPC664 has 64 KB of RAM and an internal 3-inch floppy disk drive. It was introduced on April 25, 1985 in the United Kingdom. The initial MSRP for the CPC664 was GBP £339.00/DM1198.00 with a green screen and GBP £449.00/DM1998.00 with a color monitor.

After the successful release of the CPC464, consumers continued to demand two improvements: more memory and an internal disk. For Amstrad, the latter was easier to achieve. When the CPC664 was deliberately unobtrusively introduced, the machine was positioned not only as the cheapest disk system, but even as the cheapest CP/M 2.2 machine. In the Amstrad CPC product range, the CPC664 was an addition to the CPC464 that was not discontinued or reduced in price.

Compared to the CPC464, the computer case of the CPC664 has been significantly redesigned, not only to accommodate the floppy disk drive, but also with a redesigned keyboard section. Touted as ergonomic by Amstrad's promotional materials, the keyboard is noticeably angled forward with MSX-style cursor keys above the numeric keypad. Compared to the multicolored keyboard of the CPC464, the keys of the CPC664 are kept in a much more subdued gray and light blue color scheme.

The back of the CPC664 main unit has the same connectors as the CPC464, except for an additional 12V power cable. Unlike the CPC464's cassette drive, which can be powered off from the main unit's 5V supply, the CPC664's floppy disk drive requires an additional 12V supply. This voltage had to be supplied separately by an updated version of the included green screen/color monitor (GT-65 and CTM-644 respectively).

The CPC664 was only produced for about six months. In late 1985, when the CPC6128 was introduced in Europe, Amstrad decided not to keep three models in the lineup and production of the CPC664 was discontinued.