We revisit the Floquet-Bloch eigenstates of a one-dimensional electron gas in the presence of the periodic Kronig-Penny potential and an oscillating electric field. Considering the appropriate boundary conditions for the wave function and its derivative, we derive the determining equations for the Floquet-Bloch eigenstates, which are represented by a single-infinite matrix rather than a double-infinite matrix needed for a generic potential. We numerically solve these equations, showing that

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... e appear anticrossings at the crossing points of the different Floquet bands as well as the band gaps at the edges and the center of the Brillouin zone. We also calculate the high-harmonic components of the electric current carried by the Floquet-Bloch eigenstates, showing that the harmonic spectrum shows a plateau for a strong electric field.