Additive manufacturing systems and methods used for creating 3D parts from continuous-fiber reinforced composites such as, e.g., carbon-fiber or glass-fiber pre-impregnated tape are provided. The systems and methods lay tape in successive layers and cut each layer according to a 2D slice of a 3D CAD file. During the placement of each piece of tape, a laser welds the tape to other tape, eliminating the need for post-processing of each layer. By utilizing tape instead of large fiber-reinforced sheets, the systems and methods described herein reduce waste compared to known manufacturing techniques.