An approach to generate the linearly chirped microwave waveform with simultaneous frequency and bandwidth doubling by using cascaded phase modulator and dual-output dual-parallel Mach-Zehnder modulator (DO-DPMZM) is proposed. The lightwave emitted from a laser diode is firstly modulated by a splitting parabolic signal to realize a symmetric-triangle linear frequency sweeping light. The frequency sweeping light is then sent to a DO-DPMZM driving by a radio frequency (RF) signal. By properly setting the direct current biases of two sub-modulators, single sideband modulation is realized at each output of the DO-DPMZM. By introducing a time delay in one branch of the modulator’s outputs, a linearly chirped microwave waveform with both frequency and bandwidth doubling can be generated after optical-to-electrical conversion. The central frequency and bandwidth of the generated waveform can be easily adjusted by tuning the frequency of the RF signal and electrical coding signal of the arbitrary waveform generator. The linearly chirped microwave waveforms with bandwidth of 10 GHz and central frequency of 30 GHz or bandwidth of 12 GHz and central frequency of 40 GHz are numerically generated. Due to the simple structure and flexible tunability, the proposal may find applications in future high resolution radar systems.