To acquire a high dynamic range (HDR) image of a scene, several low dynamic range (LDR) images acquired from a digital camera with different exposure times are generally fused into one HDR image to cover the entire dynamic range of the scene. However, when capturing a scene, the scene dynamic range (SDR) is unknown. Consequently, the exposure times for the LDR images need to be as varied as possible to cover the unknown SDR. This paper proposes a method to estimate the SDR using two LDR images. Using the SDR information, SDR-adaptive exposure times can then be selected to achieve the optimal HDR image. The SDR is defined as two exposure times when captured LDR images are marginally clipped to black and white, indicating the lower and upper limits of the SDR, respectively. To identify these times, two LDR images, an overexposed and an underexposed image, are captured. Using the opto-electronic conversion function of the camera used, the minimum gray level in the overexposed image is then used to estimate the exposure time to make the minimum gray level of the image just black, while the maximum gray level in the underexposed image is used to estimate the exposure time to make the maximum gray level of the image just white. By evaluating the acquired HDR image error according to the exposure times of fused LDR images for various scenes, SDR-adaptive exposure times to acquire an optimal HDR image with the minimal error are selected. Experiments confirm that the quality of an HDR image based on fusing LDR images with the proposed SDR-adaptive exposure times is similar to that of an HDR image based on fusing LDR images with conventionally chosen exposure times, even though the number of LDR images used to acquire the HDR image with the proposed method is much smaller than that used by the conventional method.