We present the X-ray spectrum of the broad-line radio galaxy Pictor A as observed by ASCA in 1996, The main objective of the observation was to detect and study the profiles of the Fe K alpha lines. The motivation was the fact that the Balmer lines of this object show well-separated displaced peaks, suggesting an origin in an accretion disk. The 0.5-10 keV X-ray spectrum is described very well by a model consisting of a power law of photon index 1.77 modified by interstellar photoelectric absorption. We find evidence for neither a soft nor a hard (Compton reflection) excess. More importantly, we do not detect an Fe K alpha line, in marked contrast with the spectra of typical Seyfert galaxies and other broad-line radio galaxies observed by ASCA. The 99% confidence upper limit on the equivalent width of an unresolved line at a rest energy of 6.4 keV is 100 eV, while for a broad line (FWHM approximate to 60,000 km s(-1)), the corresponding upper limit is 135 eV. We discuss several possible explanations for the weakness of the Fe K alpha line in Pictor A paying attention to the currently available data, on the properties of Fe K alpha lines in other broad-line radio galaxies observed by ASCA. We speculate that the absence of a hard excess (Compton reflection) or an Fe K alpha line is an indication of an accretion disk structure that is different from that of typical Seyfert galaxies, e.g., the inner disk may be an ion torus.