To increase specific contrast over background absorption in photoacoustic (PA) imaging, absorbing contrast agents can be functionalized to target specific cells. However, contrast may be severely limited because of PA signals from finite intrinsic background absorption. If background signals can be suppressed, the molecular dynamic range of contrast agents can be greatly expanded, enhancing contrast and therefore the sensitivity and specificity of PA imaging. We propose differential-absorption photoacoustic (DAPA) imaging for contrast enhancement based on suppressing undesired objects. A pump beam illuminates the imaged object, changing absorption from ground-state absorption to transient absorption. Conventional PA imaging measures ground-state absorption, while DAPA imaging detects the difference between transient and ground-state absorption by subtracting the conventional PA image from a transient PA image taken after pump beam illumination. When parameters are properly chosen so that a region of interest has finite change in absorption whereas the background has negligible change, the DAPA image will provide high contrast between the region of interest and the background. Finite changes in absorption can be obtained using photoluminescent contrast agents. Two tubes were imaged. One contains a Pt(II) octaethylporphine (PtOEP) dye solution and serves as an object of interest while the other contains an IR-783 (from Sigma-Aldrich) dye solution and serves as an object to suppress. Although the IR-783 tube dominates the conventional PA image, it is significantly overwhelmed by the PtOEP tube in the DAPA image. Analysis on excitation probability suggests that DAPA imaging has the potential to provide sufficient imaging depths for biomedical applications.