We propose an approach to generating nonlinear frequency-modulated (NLFM) microwave waveforms, which is based on controlled period-one (P1) dynamics of an optically injected semiconductor laser (OISL). When the optical injection is modulated, the OISL, which originally operates at a P1 oscillation state, acts as a microwave voltage-controlled oscillator (VCO). In the proposed system, the microwave frequency output depends closely on the optical injection strength controlled by the modulation voltage input, while the electrical modulation signal required to generate a desired NLFM microwave waveform can be calculated on the basis of the "voltage-to-frequency" transfer function of the established VCO system. Our simulations and experiments demonstrate that both single-chirp and dual-chirp NLFM microwave waveforms can be readily generated with a bandwidth up to 9 GHz. Considering peak-to-sidelobe ratio (PSLR) of the compressed pulses, the NLFM signals generated by the VCO exhibit a practical improvement of ∼13 dB when compared with LFM signals with the same bandwidth, and the tunability of the generated NLFM signals is also experimentally demonstrated.