A normal-distribution-function-shaped superconducting tunnel junction (NDF-STJ) which consists of Nb/Al-AlOx/Al/Nb has been fabricated as an X-ray detector. Current - voltage characteristics were measured at 0.4 K using three kinds of STJs, which have the dispersion parameters σ of 0.25, 0.45 and 0.75. These STJs showed very low subgap leakage current of about 5 nA. By irradiating with 5.9 keV X-rays, we obtained the spectrum of these NDF-STJs. They showed good energy resolution with small magnetic fields of below 3 mT, which is about one-tenth of those for conventional-shaped STJs.