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<p>Abstract</p><p>The binding energy of a hydrogen-like impurity in a thin size-quantized wire of the InSb/GaAs semiconductors with Kane&#8217;s dispersion law in a magnetic field<it>B</it>parallel to the wire axis has been calculated as a function of the radius of the wire and magnitude of<it>B</it>, using a variational approach. It is shown that when wire radius is less than the Bohr radius of the impurity, the nonparabolicity of dispersion law of charge carriers leads to a considerable increase of the binding energy in the magnetic field, as well as to a more rapid growth of binding energy with growth of<it>B</it>.</p>