A photonic approach that can generate triangular and rectangular waveforms is proposed. A dual-electrode Mach-Zehnder modulator (De-MZM) is used to fulfill the external optical carrier suppression (OCS) modulation of a continuous wave (CW). The follow-up four-wave mixing (FWM) in a semiconductor optical amplifier (SOA) makes four primary sidebands exist in the spectrum. Then filtering and optical carrier recovery techniques are used to construct the spectrum aligning with that of a triangular/rectangular waveform. In this work, we also elaborate the influence of errors of key device parameters, by which the feasibility and stability of the system have been verified. Based on this photonic approach, a 10 GHz full-duty-cycle triangular waveform and a 50%-duty-cycle rectangular waveform are successfully obtained. This approach provides a feasible method to generate multiple waveforms.