A deconvolution-based reconstruction algorithm is proposed to enhance the precision of the photoacoustic tomography (PAT) with the acoustic heterogeneity. This algorithm does not require the prior knowledge of the acoustic speed distribution. Firstly, a new function was constructed from detected photoacoustic signals, while the correlation between photoacoustic signals was employed to estimate the flight time of acoustic waves between two spatial positions and compensate the acoustic heterogeneity. Then the electromagnetic absorption distribution of the detected tissue can be reconstructed from this new function based on the deconvolution method. It is shown by simulation results that the reconstructed image can correctly indicate the size, location and electromagnetic absorption coefficient of detected objects when the acoustic speed variation is within 10%. This algorithm has a strong robustness to the noise. Since the acoustic speed variation of biological soft tissues is normally lower than 10%, this algorithm is an efficient reconstruction algorithm for the PAT.