Super accurate evaluation method for TiO2-doped SiO2 ultra-low-expansion glass having periodic striae associated with its fabrication process was investigated using the line-focus-beam ultrasonic material characterization (LFB-UMC) system. To obtain absolute values of leaky surface acoustic wave (LSAW) velocities measured with the LFB-UMC system, proper standard specimens of the glass for system calibration was examined. Using a specimen with a surface perpendicular to the striae plane as the standard specimen, a reliable standard LSAW velocity of 3308.18 m/s within ±0.35 m/s for the calibration was obtained regardless of influence of velocity variations due to the periodic striae. Also, we determined the accurate relationship between the TiO2 concentrations and LSAW velocities (sensitivity: -0.0601 wt%/(m/s)) so that the TiO2 concentration of the standard specimen with a LSAW velocity of 3308.18 m/s was determined to be 7.09 wt%. Furthermore, to evaluate more reliably the more homogeneous ultra-low-expansion glasses in the near future, the measurement accuracy of the LSAW velocity was improved with a method using the LFB device with a larger curvature radius R operating at lower frequency from ±0.0053% for R=1.0 mm at 225 MHz to ±0.0020% for R=2.0 mm at 75 MHz.