A new microwave photonic topology for generating a triangular waveform is presented. The concept is based on incoherent summation of two intensity modulated optical signals to generate the first and third order harmonic frequency components with the same amplitude and phase as that of an ideal triangular waveform. The proposed triangular waveform generator has a very simple and low-cost structure as it only requires the Mach Zehnder modulator in a conventional fibre optic link to be replaced by an integrated dual-polarisation modulator driven by two 90° phase difference RF signals. It also has a widely tunable repetition rate, low insertion loss and a stable performance. Experimental results demonstrate a triangular waveform with a tunable microwave-frequency repetition rate and a root mean square error value of < 0.049 when comparing with an ideal triangular waveform. The stability of the proposed triangular waveform generator is also examined experimentally.