Deep learning has proven to be an effective mechanism for computer vision tasks, especially for image denoising and burst image denoising. In this paper, we focus on solving the burst image denoising problem and aim to generate a single clean image from a burst of noisy images. We propose to combine the power of block matching and 3D filtering (BM3D) and a convolutional neural network (CNN) for burst image denoising. In particular, we design a CNN with a divide-and-conquer strategy. First, we employ BM3D to preprocess the noisy burst images. Then, the preprocessed images and noisy images are fed separately into two parallel CNN branches. The two branches produce somewhat different results. Finally, we use a light CNN block to combine the two outputs. In addition, we improve the performance by optimizing the two branches using two different constraints: a signal constraint and a noise constraint. One maps a clean signal, and the other maps the noise distribution. In addition, we adopt block matching in the network to avoid frame misalignment. Experimental results on synthetic and real noisy images show that our algorithm is competitive with other algorithms.