We numerically investigated the plasmon-induced transparency (PIT) effect in a three-dimensional plasmonic metamaterial composed of three identical rings. It is illustrated that the PIT effect appears as a result of the destructive interference between the electric dipole and the quadrupole resonance mode. By tuning gap distance, radius or rotation angle of the metamaterial, the required transmission spectra with a narrow sharp transparency peak can be realized. In particular, it is found that an on-to-off amplitude modulation of the PIT transparency window can be achieved by moving or rotating the horizontal ring. Two dips move to high frequency and low frequency regions, respectively, in the transmission spectra by moving the horizontal ring, namely, the width of transmission peak becomes larger. With the rotation of horizontal ring, both width and position of transmission peak are kept invariant. Our designed structure achieved a maximum group index of 352 in the visible frequency range, which has a significant slow light effect. Moreover, the PIT effect is explained based on the classical two-oscillator theory, which is in well agreement with the numerical results. It indicates our proposed structure and theoretical analysis may open up avenues for the tunable control of light in highly integrated optical circuits.