When a target is presented with nearby flankers in the peripheral visual field, it becomes harder to identify, which is referred to as crowding. Crowding sets a fundamental limit of object recognition in peripheral vision, preventing us from fully appreciating cluttered visual scenes. We trained adult human subjects on a crowded orientation discrimination task and investigated whether crowding could be completely eliminated by training. We discovered a two-stage learning process with this training task. In the early stage, when the target and flankers were separated beyond a certain distance, subjects acquired a relatively general ability to break crowding, as evidenced by the fact that the breaking of crowding could transfer to another crowded orientation, even a crowded motion stimulus, although the transfer to the opposite visual hemi-field was weak. In the late stage, like many classical perceptual learning effects, subjects' performance gradually improved and showed specificity to the trained orientation. We also found that, when the target and flankers were spaced too finely, training could only reduce, rather than completely eliminate, the crowding effect. This two-stage learning process illustrates a learning strategy for our brain to deal with the notoriously difficult problem of identifying peripheral objects in clutter. The brain first learned to solve the "easy and general" part of the problem (i.e., improving the processing resolution and segmenting the target and flankers) and then tackle the "difficult and specific" part (i.e., refining the representation of the target).