A noise with frequency structure, i.e. the harmonic velocity noise is investigated to describe the complicated noise environment. We studied the noise's occurrence, correlation function, power spectrum, as well as some behaviors caused by its frequency characteristics when it acts as a thermal noise. The results show that the harmonic velocity noise is band-passing in frequency spectral space with a peak frequency and the band width is determined by Γ. If a Brownian particle in a harmonic potential is driven by a thermal harmonic velocity noise, its maximum energy appears when the two frequencies are equal. This testifies that there is a dynamical resonance between the frequencies of the noise and the potential, which controls the particle's energy.