A frequency tunable optoelectronic oscillator based on a directly modulated distributed-feedback (DFB) semiconductor laser under optical injection is proposed and experimentally demonstrated. Through optical injection, the relaxation oscillation frequency of the DFB laser is enhanced and its high modulation efficiency can enable the loop oscillation with a RF threshold gain of less than 20 dB. The DFB laser is a commercial semiconductor laser with a package of 10 GHz, and its packaging limitation can be overcome by optical injection. In our scheme, neither a high-speed external modulator nor an electrical bandpass filter is required, making the system simple and low-cost. Microwave signals with a frequency tuning range from 5.98 to 15.22 GHz are generated by adjusting the injection ratio and frequency detuning between the master and slave lasers. The phase noise of the generated 9.75 GHz microwave signal is measured to be -104.8 dBc/Hz @ 10 kHz frequency offset.