This invention relates to a new and distinct everbearing variety of raspberry plant named ‘GLEAM’. The new variety is primarily adapted to the growing conditions of the central coast of California and is characterized by the following: early primocane production with medium to large sized fruit of light-red coloration. Fruit is of consistent conic shape, releases easily from receptacle and is of very good flavor. Foliage is strongly concave, medium green possessing weak rugosity and mostly 3 foliate. Primocanes have an absent or very weak waxy coat, medium thorn density and have very weak anthocyanin coloration.