A novel approach to generate tunable high-purity microwave frequency combs (MFCs) based on active mode-locking optoelectronic oscillator (OEO) is proposed and experimentally demonstrated. In the proposed method, one cavity mode of the OEO is injection-locked by a local oscillator (LO) signal resulting in single-mode oscillation. Under the assistance of an additional radio frequency signal, the MFCs generation is realized by loss modulation the single-mode oscillation. A key significance of our scheme is that no tunable filter is needed in OEO cavity. By altering the frequency of the LO signal, the MFCs center frequency can be flexibly precisely tuned over a bandwidth of 1.6 GHz. Furthermore, the high suppression of the supermode noise is obtained due to the injection locking of the OEO decreasing the required loop gain. The experimental results show that the generated MFCs maintain a large supermode noise suppression ratio over the entire tuning range.