Traditional back-projection(BP) method suffers from low resolution and high peak sidelobe level (PSL). A new method named eigenspace based adaptive beamforming (EAB) is proposed for photoacoustic computed tomography (PACT). Adaptive beamforming (AB) suppresses the interference and noise signal to improve the lateral resolution, eigenspace can further restrain the off-axis signal to eliminate the artifacts. The simulated experiment shows that the lateral resolution after BP, AB and EAB are 0.99, 0.31, and 0.31mm, respectively. The actual point targets experimental results show that the new method improves the lateral resolution by 67.9% compared with BP, which is agreed with simulated results. New method also improves the PSL by 39.6dB and 42.6dB compared with BP and AB, eliminates the artifacts and improvs imaging quality of the PACT.