The energy spectrum of electrons in narrow band gap semiconductor nanocrystals which have position dependent band gap in an external non-uniform electric field which compensate the position dependence of the band edge of the valence band potential is studied theoretically taking into account the non-parabolicity of electrons in dispersion laws. The exact solutions of the Kane equations with strong spin-orbital interaction are determined via the band-gap changes as a function of position. The band edge gap potential is taken as the ring-shaped non-spherical oscillator potential V (r) = (gamma r(2))/(2) + (a)/(r(2)) + (b)/(r(2)sin(2) theta).