This paper presents a pruning method, Reconstruction Error Aware Pruning (REAP), to reduce the redundancy of convolutional neural network models for accelerating their inference. In REAP, we have the following steps: 1) Prune the channels whose outputs are redundant and can be reconstructed from the outputs of other channels in each convolutional layer; 2) Update the weights of the remaining channels by least squares method so as to compensate the error caused by pruning. This is how we compress and accelerate the models that are initially large and slow with little degradation. The ability of REAP to maintain the model performances saves us lots of time and labors for retraining the pruned models. The challenge of REAP is the computational cost for selecting the channels to be pruned. For selecting the channels, we need to solve a huge number of least squares problems. We have developed an efficient algorithm based on biorthogonal system to obtain the solutions of those least squares problems. In the experiments, we show that REAP can conduct pruning with smaller sacrifice of the model performances than several existing methods including the previously state-of-the-art one.