||We investigate the electronic properties of the well-known one-dimensional Kronig-Penny Model with equal-spacing δ-function barriers having two distinct strengths, arranged in a Fibonacci series. The relevant Schr6dinger equation, with or without an externally applied electric field, is studied by using a Poincare map that cast the equation into a non-linear discrete difference equation. Our model, which differs from the conventional tight-binding model, is shown to exhibit many characteristics not found in prior studies. The wavefunctions in our model are found to be either localized or critical, with states in the centre of the energy band more extended than those of the edges of the bands. Also, the degree of localization is enhanced in general as the magnitude of applied electric held is increased. The energy level spacing statistics is found to be a mixture of Wigner and Poisson distributions. Our results also reveal neither the existence of Wannier-Stark ladder nor the three subdivisions for each band characteristics of the usual tight-binding model. We also show any self-similarity of the energy spectrum is broken by the electric field.