Bilateral filter based tone mapping for rendering High Dynamic Range (HDR) images can not display all details in dark or highlight areas of an image. In order to solve the problem, we propose a Local Adaptive Bilateral Filter (LABF) method having threefold improvement over the bilateral filter based method. First, since less correlation between luminance and chrominance can produce better performance, we choose YUV color space with less correlation between luminance and chrominance, and only the luminance component Y is compressed. Second, to imitate the human response to light, we adjust the logarithmic base adaptively depending on each pixel's luminance value. This strategy can provide good contrast and detail preservation in dark areas while achieving the compression of high luminance range. Third, we propose an improved center/surround method to enhance visibility in the highlight or relatively darker areas further, which is a non-linear function with a weighted average of surrounding pixel values serving a variable. The experimental results show that the proposed method LABF can obtain satisfactory results on various images with different scene contents.