The laser welding was performed for the flange joint of two overlapped coaxial circular pipes which serve as the inlet and connector pipes of STS 316L. The laser welding test finally resulted in a good penetration depth of 1.8 to 2.0 mm. On the way to get the good welding quality, two important parameters were found to be optimized. One is the focal positioning which is the offset of the laser beam focus to the exact welding seam line, which is more critical in the inner flange laser welding. When the beam spot size was deviated more than $200;{mu}m$ from the seam line, welding of two pipes is failed. The other is a gap size since a certain amount of gap is inevitable due to fabrication tolerance, or artificial allowances for smooth insertion of a pipe. However, it is required to restrict the gap allowance within 0.2mm to avoid undesirable undercut on a welding bead.