Optical generator to triangular and square waveforms with fundamental frequency and double frequency is proposed by using a polarization division multiplexing dual-parallel Mach-Zehnder modulator (PDM-DPMZM). With this approach, as the DPMZM1 is driven by an RF signal, and DPMZM2 only performs optical carrier phase shift by direct current (DC) bias without RF signal driven, triangular and square waveforms with fundamental frequency can be obtained following a polarizer and photodetector; as the two DPMZMs are both driven by an RF signal with a 90° phase difference, two waveforms with double frequency can also be generated. The proposed approach was verified by simulation. Triangular and square waveforms with repetition rates of 10 GHz and 20 GHz were generated by changing the phase difference and connection mode of the RF signal. The proposed structure features a single modulator and is filter-free, and demonstrates good tunability and large reconfigurability, which has potential applications in future high-frequency electronic systems.