Terahertz electron spin resonance (THz ESR) measurements of the S = 1/2 frustrated J1-J2 chain material NaCuMoO4(OH) were conducted on a quasi-single-crystal (QSC) sample in a pulsed high magnetic field. The QSC sample was fabricated by modulating the rotation of powder sample in a static magnetic field, resulting in three-dimensional alignment. This paper presents the fabrication method for the QSC sample which was confirmed by the Laue pattern obtained by X-ray diffraction, and the degree of orientation indicated by the anisotropic spectrum of ESR. The THz ESR measurements on the QSC sample of NaCuMoO4(OH) were performed from 0.06 THz to 1.56 THz, and we observed ESR spectra for the single axis (b-axis) above the saturation field. We demonstrate that the fabrication of magnetically aligned samples allows the observation of sharp single-axis absorption, even in the THz ESR range, which is challenging for a powder samples with a broad linewidth. Furthermore, we establish that this method is an effective approach for investigating magnetic anisotropy, even in antiferromagnetic powder samples.