A novel photonic method of linearly frequency-modulated (LFM) signal generation with high purity based on the monolithically integrated semiconductor laser (MISL) subject to the dynamical optoelectrical feedback is proposed and demonstrated in this paper. In this approach, the MISL is firstly operated in period-one state. By introducing the dynamical optoelectrical feedback to modulate the MISL, the generated LFM signals would be constantly optimized as long as the delay of the feedback loop is matched with the repetition period of the LFM signal. In this system, no additional high-speed external modulator, high-frequency electrical LFM oscillator are required, highly simplifying the framework and reducing the power consumption. In the current proof-of-concept experiment, one LFM signal with the bandwidth as large as 5.6 GHz is generated and the corresponding frequency comb contrast can be drastically improved by 51 dB. Furthermore, the effect of the delay mismatch is also discussed in this paper.