Second-harmonic phase measurement was used to determine the $x$-axis (including the direction) of $y$-cut quartz crystal by measuring the phase of the second-harmonic signal. The reference second-harmonic signal for the determination of the phase was generated from 50-$mu$m-thick reference quartz ($z$-cut quartz) in the beam path after the sample. Clear interference fringes were observed by changing the relative phase between the second-harmonic electric field from the sample and the reference by rotating the fused quartz plate in between. The second-harmonic signal with input field parallel to the $x$-axis became different from that with input field antiparallel to the $x$-axis in the presence of an interfering reference field, thus allowing us to determine the direction of the crystalline axis of quartz.