We demonstrate a 3.65 W, 40 kHz, 17.5 ns end-pumped YVO4/Nd:YVO4 ultraviolet (UV) laser at 355 nm with a beam propagation factor of 1.32 and 1.14. The frequency doubling and tripling are obtained by employing a parallel surfaces LBO crystal and a Brewster angle-cut uncoated LBO crystal in a convex–concave cavity. The arrangement allows the use of optically-uncoated third harmonic generation LBO crystal surfaces while providing wavelength separation. It is proved that the optically-uncoated THG-LBO crystal has a higher damage threshold. Pump-UV conversion efficiency of 15.5% is obtained and it is higher compared with other intra-cavity-wavelength-separation UV nanosecond lasers. By designing a convex–concave cavity structure, four advantages are showed, (1) to compensate for astigmatism caused by the Brewster angle-cut uncoated LBO crystal; (2) to offset the thermal lens effect of the gain medium; (3) to obtain a fundamental light spot size which matches with pump light spot size in the center of gain medium; (4) to obtain a small spot size in the center of the frequency conversion crystals. By employing these designs, UV beam quality Mx2 = 1.32 and My2 = 1.14 at 3.65 W are obtained.