The impulse response of the ultrasonic transducer used for detection is crucial for photoacoustic imaging with high resolution. We demonstrate a reconstruction method that allows the optical absorption distribution of a sample to be reconstructed without knowing the impulse response of the ultrasonic transducer. A convolution relationship between photoacoustic signals measured by an ultrasound transducer and optical absorption distribution is developed. Based on this theory, the projection of the optical absorption distribution of a sample can be obtained directly by deconvolving the recorded PA signal originating from a point source out of that from the sample. And a modified filtered back projection algorithm is used to reconstruct the optical absorption distribution. We constructed a photoacoustic imaging system to validate the reconstruction method and the experimental results demonstrated that the reconstructed images agreed well with the original phantom samples. The spatial resolution of the system reaches 0.3 mm.