The Arcminute Microkelvin Imager (AMI) Galactic Plane Survey is a large-area survey of the outer Galactic plane to provide arcminute resolution images at milli-Jansky sensitivity in the centimetre-wave band. Here we present the first data release of the survey, consisting of 868 deg2 of the Galactic plane, covering the area 76° 170° between latitudes of |b| 5°, at a central frequency of 15.75 GHz (1.9 cm). We describe in detail the drift-scan observations which have been used to construct the maps, including the techniques used for observing, mapping and source extraction, and summarize the properties of the finalized data sets. These observations constitute the most sensitive Galactic plane survey of large extent at centimetre-wave frequencies greater than 1.4 GHz.