To improve the photoelectric performance of an ultraviolet laser and reduce the threshold current obtained for standard structures, AlGaN-based ultraviolet laser diodes with an Al-composition graded quantum barrier layer (QBs) and an Al-composition graded n-type waveguide layer (n-WG) are proposed. A standard structure is extracted and modified from an experimental sample. Three different new structures and the standard structure are constructed and numerically investigated using PICS3D simulation software. A comparison of the L-I-V characteristic curves, band structures, carrier current density distribution, and other properties of the four structures demonstrates that ultraviolet laser diodes with an Al-composition graded QBs and Al-composition graded n-WG exhibit improved performance. Under 800 mA injection current, the optical output power can reach 775 mW, which is 35.7% higher than that obtained for the standard structure; the threshold current decreases to 62.3 mA, which is 73.6% lower than that obtained for the standard structure.