The flexural vibration behavior of elastic wave across a slender beam with locally resonant multi-oscillators structure is studied by using the transfer-matrix method and the finite element method. A simplified model is proposed, and the formulas of start and end frequencies of band gap are deduced. The more abundant and wider flexural elastic wave band gaps are found in this locally resonant multi-oscillator beam than in one oscillator beam, which can be used in the reduction of multiple-frequency vibration and noise. The frequency response of vibration in the band gap frequency range has obvious attenuation. The results of simplified model are in good agreement with results from the theory model. The research project will provide a new way for vibration reduction of beam structure.