In order to realize the multi-band tunable filtering of the metamaterial filter in the visible and near infrared bands, the ordered array of coaxial gold nanotubes is numerically simulated by using the Finite-Difference Time-Domain method. We investigate the absorption characteristics of cylindrical surface plasmons as well as gap surface plasmons in the ordered array and explore their applications in the filtering fields. Then we analyze the influence of structural parameters on the number and location of resonant wavelengths. The simulation results show that multi-band tunable filtering can be realized in the range of 600~1 700 nm by adjusting the structural parameters.