A determination method of accurate acoustical physical constants and their temperature coefficients was demonstrated for La3Ta 0.5Ga5.3Al0.2O14 (LTGA) single crystal using the ultrasonic microspectroscopy (UMS) technology combined with the resonance method. Several specimens (X-, Y-, Z-, 29.14°Y-, and 150.86°Y-cut) were prepared from an LTGA ingot. Acoustical physical constants and their temperature coefficients around room temperatures were determined using the longitudinal-and shear-wave velocities measured by the UMS system, dielectric constants, density, and thermal expansion coefficients. Measured leaky surface acoustic wave (LSAW) velocities and calculated ones using the determined constants at 23°C were compared, resulting in good agreement within-3.0 to 1.1 m/s for all propagation directions. Using four X-cut rotated Y-bar (-30°Y, 0°Y, 15°Y, 30°Y) specimens and Y-cut specimen prepared from the same ingot, the temperature coefficients in a range from-30 to 80°C were also obtained by the resonance method. Combining the temperature coefficients obtained by the resonance method with the accurate constants obtained by the UMS technology, we can determine more reliable constants and temperature coefficients.