The preparation of fuel-air mixture and its efficient, clean, and reliable combustion in spark-ignition direct-injection (SIDI) engines depend to a large extend on the complex in-cylinder air flow. It has been widely recognized that the ensemble-averaged flow field provides rather limited understanding of in-cylinder air motion due to the strong cycle-to-cycle variations. In this study, time-resolved particle image velocimetry (PIV) is utilized to measure the in-cylinder air motion in a motored single-cylinder optical engine. Then, the velocity fields from different phases (crank-angle positions during intake and compression strokes) of 200 engine cycles are analyzed using phase-invariant proper orthogonal decomposition (POD) technique. With the phase-invariant POD method, the velocity fields from different phases are decomposed into a single set of POD modes. In this manner, the POD modes can be used to represent any phase of the flow. In addition, the changes of the POD coefficients over different phases demonstrate how the flow evolves within engine cycles. Simultaneously, the coefficients from the 200 cycles for the same phase quantify the variation among different cycles. The first two phase-invariant POD modes extract the strong intake flow structures, and the third mode contains the flow structure during the compression stroke. Overall, the insight of in-cylinder flow evolution and its cycle-to-cycle variations can be further elucidated through the analysis of phase-invariant POD modes and their coefficients.