Absorption coefficient of biological tissue is an important parameter in biomedicine, but its determination remains a challenge. In this paper, we propose a method using focusing photoacoustic imaging technique and internal light irradiation of cylindrical diffusing fiber (CDF) to quantify the target optical absorption coefficient. Absorption coefficients for ink absorbers are firstly determined through photoacoustic and spectrophotometric measurements at the same excitation, which demonstrates the feasibility of this method. Also, the optical absorption coefficients of ink absorbers with several concentrations are measured. Finally, the two-dimensional scanning photoacoustic image is obtained. Optical absorption coefficient measurement and simultaneous photoacoustic imaging of absorber non-invasively are the typical characteristics of the method. This method can play a significant role for non-invasive determination of blood oxygen saturation, the absorption-based imaging and therapy.