The bilateral filter is a fundamental smoothing tool in image processing and computer vision due to its outstanding edge-preserving ability. However, the computational complexity depends on the size of the support of the spatial kernel. This drawback makes bilateral filtering time-consuming and significantly limits its applications. A novel strategy to turn the range kernel of the bilateral filter into a sum of exponential functions is proposed. As the convolution with the exponential function can be accelerated by the box filtering, the computational complexity of the bilateral thus becomes . Experimental results disclose that the proposed algorithm is competitive with the state-of-the-art algorithms in terms of filtering accuracy and computational efficiency.