A systematic investigation of the magnetization reversal and the dynamic behaviors of uncoupled Ni80Fe20 nanowires (NWs) with artificial continuous width modulation is presented. In contrast with the single resonance mode observed in the homogeneous NWs from the broadband ferromagnetic resonance spectroscopy, the NWs with continuous width modulation display three to five distinct resonance modes with increasing wire thickness in the range from 5 to 70 nm due to the nonuniform demagnetizing field. The highest frequency mode and the frequency difference between the two distinct highest modes are shown to be markedly sensitive to the NW thickness. Interestingly, we found that these modes can be described in terms of the quantization of the standing spin waves due to confined varied width. In addition, the easy axis coercive field for the width modulated NWs is much higher than homogeneous NWs of the same thickness when less than 70 nm. Our experimental results are in good qualitative agreement with the micromagnetic simulations. The results may find potential applications in the design and optimization of tunable magnonic filters.