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The magnetic field dependence of the Josephson current of a Josephson tunnel junction whose shape was a normal distribution is analyzed for superconducting tunnel junction (STJ) photon detector applications. It was found that the Josephson current of a normal distribution junction is very sensitive to the external magnetic field and follows a function of exp (-B2), while a conventional rectangular STJ exhibits the well-known Fraunhofer pattern of sin x/x. Numerical calculations show that the Josephson current of the normal distribution junction can be suppressed by an external magnetic field that is one tenth of that needed for conventional rectangular junctions. Calculations of a normal distribution junction approximated with a 1 µm mesh also show that the Josephson current is sufficiently suppressed by a small magnetic field. The effect of the misalignment of the angle between the junction and the magnetic field was evaluated. It was found that for a normal-distribution-shaped junction, misalignment of the magnetic field is allowed within ± 5°, suppressing the Josephson effect by two orders of magnitude more than that of a rectangular junction.