With the increasing complexity in power grid structures and fault characteristics, fast and accurate power grid fault diagnosis has become increasingly important for the safe and stable operation of power grids. Synchronous phasor measurement units (PMUs) are a promising approach to power grid fault diagnosis because of their synchronization, speed, and accuracy. In this study, PMU data are used as the source of fault information, and these data are transformed into polar plots. A power grid fault diagnosis method is proposed based on the polar PMU data plots and a convolutional neural network (CNN). The method is shown to reduce the computational cost and improve the efficiency of fault diagnosis. The method includes three steps. First, different types and quantities of electrical data were selected for identifying faulty equipment and fault types, and the corresponding PMU data were transformed into a polar plot using polar coordinates in different dimensions. Second, the faulty equipment detection model and the fault type classification model were constructed, and the faulty buses, lines and transformers were determined along with their various fault types based on the fault information features extracted by the CNN from the polar PMU data plots. Finally, a set of complete power grid fault diagnosis processes and a block diagram are proposed, and the validity and practicability of the proposed method are evaluated using actual measurement and simulation PMU data of the power grid.