We present imaging simulations of the Sunyaev-Zel'dovich effect of galaxy clusters for the Atacama Large Millimeter/submillimeter Array (ALMA), including the Atacama Compact Array (ACA). In its most compact configuration at 90 GHz, ALMA will resolve the intracluster medium with an effective angular resolution of 5''. It will provide a unique probe of shock fronts and relativistic electrons produced during cluster mergers at high redshifts, that are hard to spatially resolve by current and near-future X-ray detectors. The quality of image reconstruction is poor with the 12 m array alone, but improved significantly by adding ACA; the expected sensitivity of the 12 m array based on the thermal noise is not valid for the Sunyaev-Zel'dovich effect mapping unless accompanied by an ACA observation of at least equal duration. The observations above 100 GHz will become excessively time-consuming owing to the narrower beam size and the higher system temperature. On the other hand, significant improvement of the observing efficiency is expected once Band 1 is implemented in the future.