Techniques for generating microwave waveform such as square or triangle waveform have been a topic of general interest recently. Because they are important for applications in radar, measurement, instrument technology, medical imaging, etc. Usually, high quality microwave waveform is preferred as it largely determines the performance of the microwave system. In recent years, photonic microwave generation has aroused the great interest of both the research community and commercial sector all over the world, as it has the advantages of high frequency and large bandwidth. A variety of techniques for generating arbitrary waveforms have been demonstrated. In this paper, a new approach to photonic microwave waveform generation based on polarization delay interference is proposed and experimentally demonstrated, in which only one laser and Mach-Zehnder modulator (MZM) are used. In our scheme, odd-order optical sidebands can be generated by setting the bias of the MZM at the quadrature point. Thus, square waveform and triangular waveform can be generated, with a sinusoidal microwave signal applied to MZM and carefully controlling the modulation depth of MZM as well as the amount of delay on the differential delay line. A theoretical analysis of the principle of the proposed approach is performed. And optimum parameters of the photonic waveform generation are derived from numerical simulation. By simulation, the fourth order of approximation of the square waveform and triangular waveform is generated. In addition, it is proved that the scheme can generate the stable square waveform and triangular waveform by analyzing the stability of the bias and the modulation depth of the MZM. Experimentally, square waveform and triangular waveform with a repetition rate of 5 GHz are generated by carefully setting the bias and the modulation depth of the MZM, which are consistent with theoretical analyses. The scheme has the advantages of the low cost, simplicity, easy-to-tune, and it adopts the innovative technology of polarization delay interference. Hence the scheme is effective and worth spreading.