We show that harmonic driving of either the magnitude or the phase of the nearest-neighbor hopping amplitude in a p-wave superconducting wire can generate modes localized near the ends of the wire. The Floquet eigenvalues of these modes can either be equal to ±1 (which is known to occur in other models) or can lie near other values in complex conjugate pairs, which is unusual; we call the latter anomalous end modes. All the end modes have equal probabilities of particles and holes. If the amplitude of driving is small, we observe an interesting bulk-boundary correspondence for the anomalous end modes: the Floquet eigenvalues and the peaks of the Fourier transform of these end modes lie close to the Floquet eigenvalues and momenta at which the Floquet eigenvalues of the bulk system have extrema. © 2017 American Physical Society.