Nowadays, the size of DNN models has grown rapidly. To train a large model, pipeline parallelism-based frameworks partition the model across GPUs and slice each batch of data into multiple micro-batches. However, pipeline parallelism suffers from a bubble issue and low peak utilization of GPUs. Recent work tries to address the two issues, but fails to exploit the benefit of vanilla pipeline parallelism, i.e., overlapping communication with computation. In this work, we employ an elastic averaging-based framework which explores elastic averaging to add multiple parallel pipelines. To help the framework exploit the advantage of pipeline parallelism while reducing the memory footprints, we propose a schedule, advance forward propagation. Moreover, since the numbers of parallel pipelines and micro-batches are essential to the framework performance, we propose a profiling-based tuning method to automatically determine the settings. We integrate those techniques into a prototype system, namely AvgPipe, based on PyTorch. Our experiments show that AvgPipe achieves a 1.7x speedups over state-of-the-art solutions of pipeline parallelism on average.