A light-field camera captures both the intensity and the direction of incoming light(1-5). This enables a user to refocus pictures and afterwards reconstruct information on the depth of field. Research on light-field imaging can be divided into two components: acquisition and rendering. Microlens arrays have been used for acquisition, but obtaining broadband achromatic images with no spherical aberration remains challenging. Here, we describe a metalens array made of gallium nitride (GaN) nanoantennas(6) that can be used to capture light-field information and demonstrate a full-colour light-field camera devoid of chromatic aberration. The metalens array contains an array of 60 x 60 metalenses with diameters of 21.65 mu m. The camera has a diffraction-limited resolution of 1.95 mu m under white light illumination. The depth of every object in the scene can be reconstructed slice by slice from a series of rendered images with different depths of focus. Full-colour, achromatic light-field cameras could find applications in a variety of fields such as robotic vision, self-driving vehicles and virtual and augmented reality.